Question

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

score 498 · Answer 1 · 2019-05-07 02:58:12

498

Views

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

Published on 07 May 2019 - 2:58

score 1.3k · Answer 2 · 2019-06-01 13:59:18

1.3k

Views

Finding closed form of exponential generating function

Published on 01 Jun 2019 - 13:59

score 93 · Answer 3 · 2019-06-08 12:58:51

93

Views

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

Published on 08 Jun 2019 - 12:58

score 79 · Answer 4 · 2019-06-13 10:32:10

79

Views

Sum involving Stirling number of first kind

Published on 13 Jun 2019 - 10:32

score 241 · Answer 5 · 2019-06-18 01:26:19

241

Views

Probability of drawing three different colours without order

Published on 18 Jun 2019 - 1:26

score 107 · Answer 6 · 2026-03-26 08:15:26

107

Views

Why this approximation not complete with me?

Published on 26 Mar 2026 - 8:15

score 190 · Answer 7 · 2026-03-26 02:57:54

190

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 26 Mar 2026 - 2:57

score 73 · Answer 8 · 2019-07-29 03:52:59

73

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 29 Jul 2019 - 3:52

score 405 · Answer 9 · 2019-07-29 09:58:51

405

Views

Stirling numbers of the second kind and combinatorics

Published on 29 Jul 2019 - 9:58

score 216 · Answer 10 · 2019-07-30 08:06:38

216

Views

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

Published on 30 Jul 2019 - 8:06

score 91 · Answer 11 · 2019-08-06 03:02:16

91

Views

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

Published on 06 Aug 2019 - 3:02

score 173 · Answer 12 · 2019-09-05 20:33:30

173

Views

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

Published on 05 Sep 2019 - 20:33

score 100 · Answer 13 · 2019-09-08 06:47:03

100

Views

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

Published on 08 Sep 2019 - 6:47

score 178 · Answer 14 · 2019-09-09 15:59:46

178

Views

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

Published on 09 Sep 2019 - 15:59

score 40 · Answer 15 · 2019-09-23 17:35:24

40

Views

Representation of $n$-th derivative as the sum

Published on 23 Sep 2019 - 17:35

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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