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Upper bound of product of binomial coefficients

score 81 · Answer 1 · 2026-04-17 04:54:29

81

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Upper bound of product of binomial coefficients

Published on 17 Apr 2026 - 4:54

score 96 · Answer 2 · 2026-04-16 07:03:39

96

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If $ \prod_{k=0}^n (x+\frac{1}{2^k}) = \sum_{k=0} ^n a_kx^k $find $\lim_{x\to \infty}\frac{a_{n-2}}{a_{n-4}} = ?$

Published on 16 Apr 2026 - 7:03

score 71 · Answer 3 · 2026-04-16 16:19:33

71

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Proving $\sum_{k=0}^{(m-1)/2}(-1)^k{{m+1}\choose{k}}\left(\frac{m+1}{2}-k\right)^p=0$, for odd $m\geq3$ and even $2\leqslant p\leq m-1$

Published on 16 Apr 2026 - 16:19

score 249 · Answer 4 · 2026-04-14 00:04:05

249

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Sum of even binomial coefficients modulo $p$, without complex numbers

Published on 14 Apr 2026 - 0:04

score 55 · Answer 5 · 2026-04-13 10:08:48

55

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Solve for $(2t-1)^{-1}$ in binomial and hypergeometric form

Published on 13 Apr 2026 - 10:08

score 247 · Answer 6 · 2026-04-13 06:55:06

247

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simplify the sum of this binomial coefficients -- generalized gambler ruin problem

Published on 13 Apr 2026 - 6:55

score 81 · Answer 7 · 2026-04-14 21:20:28

81

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NIST Handbook Mathematical Functions: what is the binomial coefficient involving negative elements? what is the terminology for the rising factorial?

Published on 14 Apr 2026 - 21:20

score 102 · Answer 8 · 2026-04-09 01:59:40

102

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Conjectured recurrence/generating function for a binomial sum

Published on 09 Apr 2026 - 1:59

score 54 · Answer 9 · 2026-03-26 04:50:25

54

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Find the exact Pochammer notation for $\binom{-2a}{n}$ and its binomial expression

Published on 26 Mar 2026 - 4:50

score 52 · Answer 10 · 2026-04-17 10:01:53

52

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Showing $\sum_{t=0}^{k-1} \binom{k}{k-1-t}(n-1)^{k-1-t} = \sum_{t=0}^{k-1} \binom{k}{t}(n-1)^{t} $

Published on 17 Apr 2026 - 10:01

score 227 · Answer 11 · 2026-04-13 04:11:38

227

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Calculating a sum of binomial coefficients

Published on 13 Apr 2026 - 4:11

score 49 · Answer 12 · 2026-04-16 17:41:58

49

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Help evaluating the series ${n/2 + k}\choose{k}$

Published on 16 Apr 2026 - 17:41

score 52 · Answer 13 · 2026-04-17 13:11:27

52

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How Can I Compute $\sum_{k=1}^n (-1)^{k-1} \binom{n}{k} \dfrac{1}{k}$?

Published on 17 Apr 2026 - 13:11

score 65 · Answer 14 · 2026-04-11 15:11:09

65

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How to integrate cosine with a real exponent?

Published on 11 Apr 2026 - 15:11

score 57 · Answer 15 · 2026-04-13 21:12:19

57

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Solving Combinatorial Problem - Red Ball Distribution in Three Bins

Published on 13 Apr 2026 - 21:12

List Question

Upper bound of product of binomial coefficients

If $ \prod_{k=0}^n (x+\frac{1}{2^k}) = \sum_{k=0} ^n a_kx^k $find $\lim_{x\to \infty}\frac{a_{n-2}}{a_{n-4}} = ?$

Proving $\sum_{k=0}^{(m-1)/2}(-1)^k{{m+1}\choose{k}}\left(\frac{m+1}{2}-k\right)^p=0$, for odd $m\geq3$ and even $2\leqslant p\leq m-1$

Sum of even binomial coefficients modulo $p$, without complex numbers

Solve for $(2t-1)^{-1}$ in binomial and hypergeometric form

simplify the sum of this binomial coefficients -- generalized gambler ruin problem

NIST Handbook Mathematical Functions: what is the binomial coefficient involving negative elements? what is the terminology for the rising factorial?

Conjectured recurrence/generating function for a binomial sum

Find the exact Pochammer notation for $\binom{-2a}{n}$ and its binomial expression

Showing $\sum_{t=0}^{k-1} \binom{k}{k-1-t}(n-1)^{k-1-t} = \sum_{t=0}^{k-1} \binom{k}{t}(n-1)^{t} $

Calculating a sum of binomial coefficients

Help evaluating the series ${n/2 + k}\choose{k}$

How Can I Compute $\sum_{k=1}^n (-1)^{k-1} \binom{n}{k} \dfrac{1}{k}$?

How to integrate cosine with a real exponent?

Solving Combinatorial Problem - Red Ball Distribution in Three Bins

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