Question

Number of set, say $A$, of subset such that $\sum |A_i|=|\xi|$ and that $A_{ij}=A_{\ell k}\iff \ell=i\land k=j$

score 51 · Answer 1 · 2026-03-20 07:53:43

51

Views

Number of set, say $A$, of subset such that $\sum |A_i|=|\xi|$ and that $A_{ij}=A_{\ell k}\iff \ell=i\land k=j$

Published on 20 Mar 2026 - 7:53

score 388 · Answer 2 · 2026-03-22 22:38:41

388

Views

Evaluate $\sum_{k=1}^n\frac{1}{k}\binom{n}{k}$

Published on 22 Mar 2026 - 22:38

score 60 · Answer 3 · 2026-03-23 10:46:03

60

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Combinatronics Summation Series

Published on 23 Mar 2026 - 10:46

score 97 · Answer 4 · 2026-03-23 04:51:54

97

Views

Prove that: $\frac{(n+0)!}{0!}+\frac{(n+1)!}{1!}+...+\frac{(n+n)!}{n!}=\frac{(2n+1)!}{(n+1)!}$

Published on 23 Mar 2026 - 4:51

score 55 · Answer 5 · 2026-03-22 22:57:26

55

Views

Help in summing up this series involving binomial coefficients?

Published on 22 Mar 2026 - 22:57

score 51 · Answer 6 · 2026-03-24 23:46:01

51

Views

Pascal's triangle shows the factors of a row n.

Published on 24 Mar 2026 - 23:46

score 91 · Answer 7 · 2026-03-23 06:56:19

91

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Closed form of $\sum_{k=0}^p \binom{k+m-1}{m-1}?$

Published on 23 Mar 2026 - 6:56

score 73 · Answer 8 · 2026-03-23 07:46:09

73

Views

Closed form or estimate for $m-$fold sum of binomial coefficients

Published on 23 Mar 2026 - 7:46

score 314 · Answer 9 · 2026-03-23 13:22:07

314

Views

Show that $ \sum_{k=0}^{n} \binom{2n+1}{2k} 3^k $ is divisible by $2^n$

Published on 23 Mar 2026 - 13:22

score 73 · Answer 10 · 2026-03-22 19:47:51

73

Views

Bound for binomial sum

Published on 22 Mar 2026 - 19:47

score 248 · Answer 11 · 2026-03-23 04:08:59

248

Views

Binomial Expansion Find: $\sum_{k=0}^n\binom{n}{k} 2^k $

Published on 23 Mar 2026 - 4:08

score 111 · Answer 12 · 2026-03-22 18:01:42

111

Views

Is it true that $ \sum_{k=0}^{(2q+1)n+q} \binom{2\left((2q+1)n+q\right)+1}{2k} 3^k $ is divisible by $\sum_{k=0}^{q} \binom{2q+1}{2k} 3^k $

Published on 22 Mar 2026 - 18:01

score 619 · Answer 13 · 2026-03-23 11:14:29

619

Views

Combinatorial interpretation of $\sum_{k=0}^{\min(p,q)}{p\choose k}{q\choose k}{n+k\choose p+q}={n\choose p}{n\choose q}$

Published on 23 Mar 2026 - 11:14

score 57 · Answer 14 · 2026-03-22 18:24:16

57

Views

Sum of Binomial Coefficients?

Published on 22 Mar 2026 - 18:24

score 74 · Answer 15 · 2026-03-23 08:17:29

74

Views

Trouble with this equality

Published on 23 Mar 2026 - 8:17

List Question

Number of set, say $A$, of subset such that $\sum |A_i|=|\xi|$ and that $A_{ij}=A_{\ell k}\iff \ell=i\land k=j$

Evaluate $\sum_{k=1}^n\frac{1}{k}\binom{n}{k}$

Combinatronics Summation Series

Prove that: $\frac{(n+0)!}{0!}+\frac{(n+1)!}{1!}+...+\frac{(n+n)!}{n!}=\frac{(2n+1)!}{(n+1)!}$

Help in summing up this series involving binomial coefficients?

Pascal's triangle shows the factors of a row n.

Closed form of $\sum_{k=0}^p \binom{k+m-1}{m-1}?$

Closed form or estimate for $m-$fold sum of binomial coefficients

Show that $ \sum_{k=0}^{n} \binom{2n+1}{2k} 3^k $ is divisible by $2^n$

Bound for binomial sum

Binomial Expansion Find: $\sum_{k=0}^n\binom{n}{k} 2^k $

Is it true that $ \sum_{k=0}^{(2q+1)n+q} \binom{2\left((2q+1)n+q\right)+1}{2k} 3^k $ is divisible by $\sum_{k=0}^{q} \binom{2q+1}{2k} 3^k $

Combinatorial interpretation of $\sum_{k=0}^{\min(p,q)}{p\choose k}{q\choose k}{n+k\choose p+q}={n\choose p}{n\choose q}$

Sum of Binomial Coefficients?

Trouble with this equality

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