List questions from binomial-coefficients

Published on 16 Apr 2026 - 6:52

244

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Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$

Published on 26 Mar 2026 - 4:35

71

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Closed-form solution for $f(n) = \sum_{k>0}\binom{n}{2k}x^{k}$ without $\sqrt{x}$

Published on 13 Apr 2026 - 5:21

895

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$\sum_{i=0}^{k} \binom{m}{i}\binom{n}{k-i} =\binom{m+n}{k}$

Published on 17 Apr 2026 - 5:42

135

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Limit of $\frac{1}{n}\log({n\choose np})$ without using Stirling's formula

Published on 13 Apr 2026 - 19:31

159

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Limit of quotient of summations involving special binomial coefficients

Published on 12 Apr 2026 - 22:47

593

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Binomial coefficients bounded by entropy exponential

Published on 11 Apr 2026 - 11:09

70

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Using Stirling's formula to uniformly bound Bernoulli success probabilities (part 2)

Published on 14 Apr 2026 - 11:00

806

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Finding the coefficient of a power series

Published on 17 Apr 2026 - 0:44

227

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Proof By Induction Using Binomial Coefficients

Published on 12 Apr 2026 - 1:42

4.5k

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Binomial Expansion where N is negative

Published on 11 Apr 2026 - 14:53

59

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What is $\binom{n}{-k}$?

Published on 10 Apr 2026 - 20:58

630

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Curious Binomial Coefficient Identity

Published on 11 Apr 2026 - 21:02

194

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The maximum of $\binom{n}{x+1}-\binom{n}{x}$

Published on 17 Apr 2026 - 2:06

2k

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Proving the sum of squares of sine and cosine using the Cauchy product formula

Published on 09 Apr 2026 - 10:04

List Question

Hypergeometric 2F1 with negative c

Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$

Closed-form solution for $f(n) = \sum_{k>0}\binom{n}{2k}x^{k}$ without $\sqrt{x}$

$\sum_{i=0}^{k} \binom{m}{i}\binom{n}{k-i} =\binom{m+n}{k}$

Limit of $\frac{1}{n}\log({n\choose np})$ without using Stirling's formula

Limit of quotient of summations involving special binomial coefficients

Binomial coefficients bounded by entropy exponential

Using Stirling's formula to uniformly bound Bernoulli success probabilities (part 2)

Finding the coefficient of a power series

Proof By Induction Using Binomial Coefficients

Binomial Expansion where N is negative

What is $\binom{n}{-k}$?

Curious Binomial Coefficient Identity

The maximum of $\binom{n}{x+1}-\binom{n}{x}$

Proving the sum of squares of sine and cosine using the Cauchy product formula

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