Question

Number of subsets of an n-element set, such that the cardinality of each subset is divisible by 3.

score 502 · Answer 1 · 2026-04-14 11:37:30

502

Views

Number of subsets of an n-element set, such that the cardinality of each subset is divisible by 3.

Published on 14 Apr 2026 - 11:37

score 1.3k · Answer 2 · 2026-04-07 17:11:01

1.3k

Views

Finding closed form of exponential generating function

Published on 07 Apr 2026 - 17:11

score 96 · Answer 3 · 2026-04-14 13:33:32

96

Views

Proof that $\sum_{k=1}^n(-1)^k(k-1)!{n \brace k} = 0$ in use combinatoric interpretation

Published on 14 Apr 2026 - 13:33

score 82 · Answer 4 · 2026-04-12 05:57:45

82

Views

Sum involving Stirling number of first kind

Published on 12 Apr 2026 - 5:57

score 244 · Answer 5 · 2026-04-14 16:07:44

244

Views

Probability of drawing three different colours without order

Published on 14 Apr 2026 - 16:07

score 110 · Answer 6 · 2026-05-10 13:47:19

110

Views

Why this approximation not complete with me?

Published on 10 May 2026 - 13:47

score 191 · Answer 7 · 2026-04-16 04:15:02

191

Views

How to prove $ \frac{\ln^k(1+x)}{k!}=\sum_{n=k}^\infty(-1)^{n-k} \begin{bmatrix} n \\ k \end{bmatrix}\frac{x^n}{n!}$

Published on 16 Apr 2026 - 4:15

score 76 · Answer 8 · 2026-04-15 03:02:56

76

Views

How to calculate the sum of a finite series: $P(k) = \sum_{i=1}^{k} S_2(m,i) \frac{n!}{n^m (n-i)!}$?

Published on 15 Apr 2026 - 3:02

score 408 · Answer 9 · 2026-04-12 13:04:19

408

Views

Stirling numbers of the second kind and combinatorics

Published on 12 Apr 2026 - 13:04

score 218 · Answer 10 · 2026-04-12 07:56:16

218

Views

What is the generalised recurrence for Stirling numbers of the second kind?

Published on 12 Apr 2026 - 7:56

score 94 · Answer 11 · 2026-04-13 16:13:14

94

Views

Generating polynom for stirling numbers of second kind - Where's my mistake?

Published on 13 Apr 2026 - 16:13

score 176 · Answer 12 · 2026-04-16 00:51:07

176

Views

Large $n,k$ asymptotics for Stirling numbrs of the first kind $\left[ \matrix{n\\k}\right]$

Published on 16 Apr 2026 - 0:51

score 103 · Answer 13 · 2026-04-14 13:18:21

103

Views

"Solving" for $n$ the equation ${2n\brack n}=k$ (Stirling numbers of the first kind)

Published on 14 Apr 2026 - 13:18

score 181 · Answer 14 · 2026-04-15 09:52:16

181

Views

Maximizing the number of $n$-tuples in $\{1,...,m\}^n$ such that . . .

Published on 15 Apr 2026 - 9:52

score 43 · Answer 15 · 2026-04-12 23:59:31

43

Views

Representation of $n$-th derivative as the sum

Published on 12 Apr 2026 - 23:59

List Question

Number of subsets of an n-element set, such that the cardinality of each subset is divisible by 3.

Finding closed form of exponential generating function

Proof that $\sum_{k=1}^n(-1)^k(k-1)!{n \brace k} = 0$ in use combinatoric interpretation

Sum involving Stirling number of first kind

Probability of drawing three different colours without order

Why this approximation not complete with me?

How to prove $ \frac{\ln^k(1+x)}{k!}=\sum_{n=k}^\infty(-1)^{n-k} \begin{bmatrix} n \\ k \end{bmatrix}\frac{x^n}{n!}$

How to calculate the sum of a finite series: $P(k) = \sum_{i=1}^{k} S_2(m,i) \frac{n!}{n^m (n-i)!}$?

Stirling numbers of the second kind and combinatorics

What is the generalised recurrence for Stirling numbers of the second kind?

Generating polynom for stirling numbers of second kind - Where's my mistake?

Large $n,k$ asymptotics for Stirling numbrs of the first kind $\left[ \matrix{n\\k}\right]$

"Solving" for $n$ the equation ${2n\brack n}=k$ (Stirling numbers of the first kind)

Maximizing the number of $n$-tuples in $\{1,...,m\}^n$ such that . . .

Representation of $n$-th derivative as the sum

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