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 53 · Answer 1 · 2026-05-06 02:40:48

53

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 06 May 2026 - 2:40

score 391 · Answer 2 · 2026-05-10 14:56:20

391

Views

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

Published on 10 May 2026 - 14:56

score 66 · Answer 3 · 2026-05-10 19:17:20

66

Views

Combinatronics Summation Series

Published on 10 May 2026 - 19:17

score 100 · Answer 4 · 2026-05-10 15:52:38

100

Views

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

Published on 10 May 2026 - 15:52

score 57 · Answer 5 · 2026-05-06 14:20:37

57

Views

Help in summing up this series involving binomial coefficients?

Published on 06 May 2026 - 14:20

score 53 · Answer 6 · 2026-05-10 16:13:13

53

Views

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

Published on 10 May 2026 - 16:13

score 93 · Answer 7 · 2026-05-05 13:10:11

93

Views

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

Published on 05 May 2026 - 13:10

score 75 · Answer 8 · 2026-05-05 14:31:29

75

Views

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

Published on 05 May 2026 - 14:31

score 316 · Answer 9 · 2026-05-05 11:35:36

316

Views

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

Published on 05 May 2026 - 11:35

score 76 · Answer 10 · 2026-05-07 13:38:53

76

Views

Bound for binomial sum

Published on 07 May 2026 - 13:38

score 250 · Answer 11 · 2026-05-05 03:56:47

250

Views

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

Published on 05 May 2026 - 3:56

score 113 · Answer 12 · 2026-05-05 03:28:39

113

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 05 May 2026 - 3:28

score 623 · Answer 13 · 2026-05-06 12:09:22

623

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 06 May 2026 - 12:09

score 60 · Answer 14 · 2026-05-05 14:45:09

60

Views

Sum of Binomial Coefficients?

Published on 05 May 2026 - 14:45

score 78 · Answer 15 · 2026-05-05 15:26:45

78

Views

Trouble with this equality

Published on 05 May 2026 - 15:26

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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