Question

Are there Stirling numbers of $z$-kind?

score 107 · Answer 1 · 2026-02-23 08:43:04

107

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Are there Stirling numbers of $z$-kind?

Published on 23 Feb 2026 - 8:43

score 251 · Answer 2 · 2026-03-28 20:14:51

251

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Number of ways to send out $k$ distinct postcards to $n$ friends if we require each friends receives at least $1$ post card.

Published on 28 Mar 2026 - 20:14

score 119 · Answer 3 · 2022-09-02 08:16:01

119

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Roll a fair, six-sided die 10 times. What is the probability that each side appears at least once?

Published on 02 Sep 2022 - 8:16

score 244 · Answer 4 · 2022-09-04 18:08:28

244

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A formula for stirling number of first kind

Published on 04 Sep 2022 - 18:08

score 73 · Answer 5 · 2022-09-06 20:05:58

73

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What happens with indexes in this proof?

Published on 06 Sep 2022 - 20:05

score 302 · Answer 6 · 2026-03-25 23:37:47

302

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Strange polynomial analog of the Bell numbers

Published on 25 Mar 2026 - 23:37

score 291 · Answer 7 · 2022-10-04 05:26:18

291

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Is there a closed form expression for $\sum_{1\le i_1 \le i_2 \le \dots \le i_k \le n} i_1 i_2 \dots i_k$?

Published on 04 Oct 2022 - 5:26

score 79 · Answer 8 · 2022-10-08 10:28:58

79

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Help me proving $\sum_{k=0}^n {n \choose k}k^r x^k = \sum_{j=0}^{r} {n \choose j} j! (1+x)^{n-j} x^j S(r,j)$

Published on 08 Oct 2022 - 10:28

score 127 · Answer 9 · 2026-03-29 22:25:21

127

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Finding a closed form for this sequence ((A080416))

Published on 29 Mar 2026 - 22:25

score 797 · Answer 10 · 2022-11-12 07:15:57

797

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Combinatorial proof of Stirling Numbers of the second kind

Published on 12 Nov 2022 - 7:15

score 36 · Answer 11 · 2022-11-14 15:55:43

36

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Probability of having at least one element from a class in a subsample

Published on 14 Nov 2022 - 15:55

score 114 · Answer 12 · 2022-12-07 02:51:37

114

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Explicit formula for Stirling numbers

Published on 07 Dec 2022 - 2:51

score 48 · Answer 13 · 2022-12-10 16:07:56

48

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How to Construct a Interpolating Function f(n) such that f(1)=a1, f(2)=a2, ..., f(n)=an, and f(x)=0 for all the other integer x?

Published on 10 Dec 2022 - 16:07

score 168 · Answer 14 · 2022-12-13 02:28:08

168

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Generating Functions and Equivalent Sums

Published on 13 Dec 2022 - 2:28

score 231 · Answer 15 · 2022-12-22 07:37:17

231

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Show the following holds for $c\leq 1$: $e^{ck^2/n} \frac{(n!)^2}{(n+k)!(n-k)!} \leq M, \quad \text{for } k = 1, \dots, n.$ for some constant $M$

Published on 22 Dec 2022 - 7:37

List Question

Are there Stirling numbers of $z$-kind?

Number of ways to send out $k$ distinct postcards to $n$ friends if we require each friends receives at least $1$ post card.

Roll a fair, six-sided die 10 times. What is the probability that each side appears at least once?

A formula for stirling number of first kind

What happens with indexes in this proof?

Strange polynomial analog of the Bell numbers

Is there a closed form expression for $\sum_{1\le i_1 \le i_2 \le \dots \le i_k \le n} i_1 i_2 \dots i_k$?

Help me proving $\sum_{k=0}^n {n \choose k}k^r x^k = \sum_{j=0}^{r} {n \choose j} j! (1+x)^{n-j} x^j S(r,j)$

Finding a closed form for this sequence ((A080416))

Combinatorial proof of Stirling Numbers of the second kind

Probability of having at least one element from a class in a subsample

Explicit formula for Stirling numbers

How to Construct a Interpolating Function f(n) such that f(1)=a1, f(2)=a2, ..., f(n)=an, and f(x)=0 for all the other integer x?

Generating Functions and Equivalent Sums

Show the following holds for $c\leq 1$: $e^{ck^2/n} \frac{(n!)^2}{(n+k)!(n-k)!} \leq M, \quad \text{for } k = 1, \dots, n.$ for some constant $M$

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