Question

Solving inequalities regarding Stirling numbers

score 342 · Answer 1 · 2016-03-06 14:25:57

342

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Solving inequalities regarding Stirling numbers

Published on 06 Mar 2016 - 14:25

score 71 · Answer 2 · 2016-03-08 09:28:23

71

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Please explain the algebraic manipulations between these two formulas for Stirling numbers of the second kind

Published on 08 Mar 2016 - 9:28

score 45 · Answer 3 · 2016-03-26 20:36:34

45

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How many ways are for K people to work a one-day shift for N days so each of them works at least one day

Published on 26 Mar 2016 - 20:36

score 172 · Answer 4 · 2016-03-29 18:37:04

172

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How to solve the following limit using mathematics Stirling $\lim\limits_{n\to \infty}\frac{n!}{n^ne^{-n}\sqrt{2\pi n}}=1$

Published on 29 Mar 2016 - 18:37

score 2.7k · Answer 5 · 2016-03-30 01:02:52

2.7k

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Formula for finding the nth number in this sequence: $[0, 1, 3, 11, 50, 274...]$?

Published on 30 Mar 2016 - 1:02

score 78 · Answer 6 · 2016-03-30 17:06:29

78

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Proving that $\sum_{n=1}^{\infty}S(n,n-2)x^n = \frac{x^3(1+2x)}{(1-x)^5}$

Published on 30 Mar 2016 - 17:06

score 169 · Answer 7 · 2016-04-03 20:29:00

169

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Showing that $x^n=\sum_{k=1}^{n}{n\brace k}(x)(x-1)\ldots (x-k+1)$ holds for all numbers, not just positive integers

Published on 03 Apr 2016 - 20:29

score 521 · Answer 8 · 2016-04-12 19:21:23

If $S(n, n - 3) = a \binom n 4 + b \binom n 5 + c \binom n 6$, find $a, b, c$ (where $S(n, k)$ denotes a Stirling number of the second kind)

score 95 · Answer 9 · 2016-04-20 13:24:17

95

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Why $S(n,k)$ is the coefficient of $x^{n-k}$ in $\prod_{t=0}^{k}(1+tx+t^2x^2+\cdots+t^nx^n)$?

Published on 20 Apr 2016 - 13:24

score 478 · Answer 10 · 2016-04-20 16:09:57

478

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Interpretation of the unsigned Stirling number of the first kind.

Published on 20 Apr 2016 - 16:09

score 397 · Answer 11 · 2016-04-21 17:14:01

397

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Stirling numbers of first kind

Published on 21 Apr 2016 - 17:14

score 1.9k · Answer 12 · 2016-04-28 07:51:45

1.9k

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A sum of Stirling numbers of the second kind

Published on 28 Apr 2016 - 7:51

score 442 · Answer 13 · 2026-03-28 08:09:59

442

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Number of Blocks of Size $i$ in Set Partitions

Published on 28 Mar 2026 - 8:09

score 175 · Answer 14 · 2016-05-02 00:36:40

175

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Combinatorial proof or meaning of the identity

Published on 02 May 2016 - 0:36

score 194 · Answer 15 · 2016-05-03 08:21:06

194

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Stirling number of first kind monotone for a half

Published on 03 May 2016 - 8:21

List Question

Solving inequalities regarding Stirling numbers

Please explain the algebraic manipulations between these two formulas for Stirling numbers of the second kind

How many ways are for K people to work a one-day shift for N days so each of them works at least one day

How to solve the following limit using mathematics Stirling $\lim\limits_{n\to \infty}\frac{n!}{n^ne^{-n}\sqrt{2\pi n}}=1$

Formula for finding the nth number in this sequence: $[0, 1, 3, 11, 50, 274...]$?

Proving that $\sum_{n=1}^{\infty}S(n,n-2)x^n = \frac{x^3(1+2x)}{(1-x)^5}$

Showing that $x^n=\sum_{k=1}^{n}{n\brace k}(x)(x-1)\ldots (x-k+1)$ holds for all numbers, not just positive integers

If $S(n, n - 3) = a \binom n 4 + b \binom n 5 + c \binom n 6$, find $a, b, c$ (where $S(n, k)$ denotes a Stirling number of the second kind)

Why $S(n,k)$ is the coefficient of $x^{n-k}$ in $\prod_{t=0}^{k}(1+tx+t^2x^2+\cdots+t^nx^n)$?

Interpretation of the unsigned Stirling number of the first kind.

Stirling numbers of first kind

A sum of Stirling numbers of the second kind

Number of Blocks of Size $i$ in Set Partitions

Combinatorial proof or meaning of the identity

Stirling number of first kind monotone for a half

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