# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 25 results; page 1/1. ## Question 23051: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0026`; number: 23051 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0026/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0026.json) ## Question 23052: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0027`; number: 23052 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0027/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0027.json) ## Question 23053: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0028`; number: 23053 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0028/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0028.json) ## Question 23054: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0029`; number: 23054 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0029/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0029.json) ## Question 23055: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0030`; number: 23055 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0030/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0030.json) ## Question 23056: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0031`; number: 23056 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0031/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0031.json) ## Question 23057: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0032`; number: 23057 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0032/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0032.json) ## Question 23058: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0033`; number: 23058 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0033/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0033.json) ## Question 23059: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0034`; number: 23059 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0034/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0034.json) ## Question 23060: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0035`; number: 23060 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0035/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0035.json) ## Question 23061: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0036`; number: 23061 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0036/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0036.json) ## Question 23062: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0037`; number: 23062 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0037/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0037.json) ## Question 23063: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0038`; number: 23063 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0038/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0038.json) ## Question 23064: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0039`; number: 23064 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0039/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0039.json) ## Question 23065: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0040`; number: 23065 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0040/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0040.json) ## Question 23066: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0041`; number: 23066 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0041/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0041.json) ## Question 23067: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0042`; number: 23067 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0042/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0042.json) ## Question 23068: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0043`; number: 23068 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0043/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0043.json) ## Question 23069: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0044`; number: 23069 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0044/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0044.json) ## Question 23070: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0045`; number: 23070 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0045/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0045.json) ## Question 23071: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0046`; number: 23071 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0046/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0046.json) ## Question 23072: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0047`; number: 23072 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0047/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0047.json) ## Question 23073: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0048`; number: 23073 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0048/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0048.json) ## Question 23074: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0049`; number: 23074 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0049/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0049.json) ## Question 23075: Exact Falling Factorials Preserve Low-to-High Derivative Coefficients - ID: `q-20261014-advance-20261111-r02-higher-order-derivative-0050`; number: 23075 - Processing: second_context_reviewed - MKO: [mko-higher-order-derivative](/en/mko/mko-higher-order-derivative/) - Family: [qf-mod42-higher-polynomial-nth-derivative](/en/explore/?family=qf-mod42-higher-polynomial-nth-derivative) - Batch: [batch-20261014-advance-20261111-r02-higher-order-derivative-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r02-higher-order-derivative-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0050/) / [Markdown](/en/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0050.json)