Question

Cubes of binomial coefficients $\sum_{n=0}^{\infty}{{2n\choose n}^3\over 2^{6n}}={\pi\over \Gamma^4\left({3\over 4}\right)}$

score 736 · Answer 1 · 2026-04-16 01:41:07

736

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Cubes of binomial coefficients $\sum_{n=0}^{\infty}{{2n\choose n}^3\over 2^{6n}}={\pi\over \Gamma^4\left({3\over 4}\right)}$

Published on 16 Apr 2026 - 1:41

score 38 · Answer 2 · 2026-04-15 05:05:29

38

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Find a set whose size is $k!{{n-1}\choose{k-1}}$.

Published on 15 Apr 2026 - 5:05

score 2.2k · Answer 3 · 2026-04-14 10:42:15

2.2k

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Alternating row sums of Pascal's Triangle

Published on 14 Apr 2026 - 10:42

score 3.8k · Answer 4 · 2026-04-17 08:03:21

3.8k

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the coefficient of $ x^{n-1}$ in $(x+3)^n+(x+3)^{n-1}(x+2)+(x+3)^{n-2}(x+2)^2\cdots(x+2)^n$

Published on 17 Apr 2026 - 8:03

score 1.2k · Answer 5 · 2026-04-12 06:34:17

1.2k

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Pascal's Triangle's different usages

Published on 12 Apr 2026 - 6:34

score 2.5k · Answer 6 · 2026-04-16 11:56:15

2.5k

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The index 'n' of binomial $(\frac{x}{5}+\frac{2}{5})^n$ if the 9th term has numerically the greatest coefficient

Published on 16 Apr 2026 - 11:56

score 77 · Answer 7 · 2026-04-16 04:40:39

77

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Find the sum of this series of coefficients of $(1+x+x^2)^n$.

Published on 16 Apr 2026 - 4:40

score 174 · Answer 8 · 2026-04-09 11:07:28

174

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Multiple Binomial Rounds with Changing Probability

Published on 09 Apr 2026 - 11:07

score 272 · Answer 9 · 2026-04-11 23:23:41

272

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Finding the value of $\sum\frac{2r+3}{r+1}\binom{n}{r}$

Published on 11 Apr 2026 - 23:23

score 89 · Answer 10 · 2026-04-15 08:29:09

89

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Find the value of $\sum\binom{6n}{2k-1}(-3)^k$

Published on 15 Apr 2026 - 8:29

score 441 · Answer 11 · 2026-04-11 01:53:32

441

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Partial sum of binomial coefficients with multiplier.

Published on 11 Apr 2026 - 1:53

score 142 · Answer 12 · 2026-04-12 22:38:59

142

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Closed form for the sum $\sum_{l=0}^k(-1)^l \binom{m}{k-l}\binom{n+k-1}{l}$

Published on 12 Apr 2026 - 22:38

score 52 · Answer 13 · 2026-04-08 17:44:22

52

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help in combination formula

Published on 08 Apr 2026 - 17:44

score 89 · Answer 14 · 2026-04-12 17:44:46

89

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Binomial Coefficient Review

Published on 12 Apr 2026 - 17:44

score 75 · Answer 15 · 2026-04-16 01:18:23

75

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Find $\sum_{i=0}^{n}\sum_{j=i}^n(\binom{n}{i}+\binom{n}{j})$

Published on 16 Apr 2026 - 1:18

List Question

Cubes of binomial coefficients $\sum_{n=0}^{\infty}{{2n\choose n}^3\over 2^{6n}}={\pi\over \Gamma^4\left({3\over 4}\right)}$

Find a set whose size is $k!{{n-1}\choose{k-1}}$.

Alternating row sums of Pascal's Triangle

the coefficient of $ x^{n-1}$ in $(x+3)^n+(x+3)^{n-1}(x+2)+(x+3)^{n-2}(x+2)^2\cdots(x+2)^n$

Pascal's Triangle's different usages

The index 'n' of binomial $(\frac{x}{5}+\frac{2}{5})^n$ if the 9th term has numerically the greatest coefficient

Find the sum of this series of coefficients of $(1+x+x^2)^n$.

Multiple Binomial Rounds with Changing Probability

Finding the value of $\sum\frac{2r+3}{r+1}\binom{n}{r}$

Find the value of $\sum\binom{6n}{2k-1}(-3)^k$

Partial sum of binomial coefficients with multiplier.

Closed form for the sum $\sum_{l=0}^k(-1)^l \binom{m}{k-l}\binom{n+k-1}{l}$

help in combination formula

Binomial Coefficient Review

Find $\sum_{i=0}^{n}\sum_{j=i}^n(\binom{n}{i}+\binom{n}{j})$

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