Question

How are the Bell numbers related to this exponential series?

score 506 · Answer 1 · 2026-03-25 12:53:35

506

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How are the Bell numbers related to this exponential series?

Published on 25 Mar 2026 - 12:53

score 63 · Answer 2 · 2026-03-27 12:03:10

63

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Is $S(n,k)= \sum_{r=k-1}^{n-1} \binom{n-1}{r} S(r,k-1)=\sum_{r=k-1}^{n-1} k^{r-1} S(r,k-1)$?

Published on 27 Mar 2026 - 12:03

score 54 · Answer 3 · 2023-02-03 18:31:07

54

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Recurrence Relation on Stirling Numbers of the First Kind

Published on 03 Feb 2023 - 18:31

score 81 · Answer 4 · 2023-02-27 22:59:46

81

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Combinatorial proof of $S(n,n-2)=\binom{n}{3}+\frac{1}{2}\binom{n}{2}\binom{n-2}{2}$ when $n \ge 4$

Published on 27 Feb 2023 - 22:59

score 65 · Answer 5 · 2023-03-04 03:43:06

65

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Using Stirling numbers to find integers $a_k$ such that $4x^4-2x^2+5x-1=\sum_{k\ge 0}a_k(x)_k$?

Published on 04 Mar 2023 - 3:43

score 158 · Answer 6 · 2023-03-05 23:16:54

158

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Inequality for triple product of Stirling numbers

Published on 05 Mar 2023 - 23:16

score 64 · Answer 7 · 2026-03-26 16:07:08

64

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Given $x$ find minimum positive $N$ for which the following is composite $ 1^x+2^x+3^x+4^x+\cdots+N^x $

Published on 26 Mar 2026 - 16:07

score 47 · Answer 8 · 2023-04-07 00:49:37

47

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Showing $\sum_{i=0}^n c(n,i) = n!$ with cardinality of Symmetric Group

Published on 07 Apr 2023 - 0:49

score 78 · Answer 9 · 2026-02-23 07:47:41

78

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A problem involving an identity relating Bernoulli numbers and Stirling numbers of the first kind

Published on 23 Feb 2026 - 7:47

score 97 · Answer 10 · 2023-04-18 19:48:11

97

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Cleaner form for transformation involving Stirling numbers

Published on 18 Apr 2023 - 19:48

score 58 · Answer 11 · 2023-04-19 20:59:58

58

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$10$ students, $16$ lessons, each lesson one student is chosen to be asked, probability that every student will be asked after $16$ lessons

Published on 19 Apr 2023 - 20:59

score 55 · Answer 12 · 2023-04-25 10:12:15

55

Views

Number of integer sequences with specific conditions proof

Published on 25 Apr 2023 - 10:12

score 52 · Answer 13 · 2023-05-01 17:03:28

52

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Simple integer sequence with unknown direct generator

Published on 01 May 2023 - 17:03

score 106 · Answer 14 · 2026-03-27 11:37:32

106

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Alternative roots of generalized Laguerre polynomials

Published on 27 Mar 2026 - 11:37

score 104 · Answer 15 · 2023-05-17 21:01:46

104

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limit to infinite of a factorial number

Published on 17 May 2023 - 21:01

List Question

How are the Bell numbers related to this exponential series?

Is $S(n,k)= \sum_{r=k-1}^{n-1} \binom{n-1}{r} S(r,k-1)=\sum_{r=k-1}^{n-1} k^{r-1} S(r,k-1)$?

Recurrence Relation on Stirling Numbers of the First Kind

Combinatorial proof of $S(n,n-2)=\binom{n}{3}+\frac{1}{2}\binom{n}{2}\binom{n-2}{2}$ when $n \ge 4$

Using Stirling numbers to find integers $a_k$ such that $4x^4-2x^2+5x-1=\sum_{k\ge 0}a_k(x)_k$?

Inequality for triple product of Stirling numbers

Given $x$ find minimum positive $N$ for which the following is composite $ 1^x+2^x+3^x+4^x+\cdots+N^x $

Showing $\sum_{i=0}^n c(n,i) = n!$ with cardinality of Symmetric Group

A problem involving an identity relating Bernoulli numbers and Stirling numbers of the first kind

Cleaner form for transformation involving Stirling numbers

$10$ students, $16$ lessons, each lesson one student is chosen to be asked, probability that every student will be asked after $16$ lessons

Number of integer sequences with specific conditions proof

Simple integer sequence with unknown direct generator

Alternative roots of generalized Laguerre polynomials

limit to infinite of a factorial number

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