Question

The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$

score 199 · Answer 1 · 2026-05-07 12:43:02

199

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The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$

Published on 07 May 2026 - 12:43

score 71 · Answer 2 · 2026-05-05 15:32:25

71

Views

How to multiply generating functions with $x^n$ and $x^{5n}$ and $x^{2n}$

Published on 05 May 2026 - 15:32

score 176 · Answer 3 · 2026-05-02 23:51:36

176

Views

Relationship between the generating functions of sequences $(a_n),(b_n)$ given $b_n=\sum^n_{i=1}a_i$.

Published on 02 May 2026 - 23:51

score 312 · Answer 4 · 2026-05-05 05:34:26

312

Views

Double-exponential sum (maybe it telescopes?)

Published on 05 May 2026 - 5:34

score 106 · Answer 5 · 2026-05-05 07:29:50

106

Views

Solve recurrence equation: $a_{n}=(n-1)(a_{n-1}+a_{n-2})$

Published on 05 May 2026 - 7:29

score 331 · Answer 6 · 2026-05-05 22:04:47

331

Views

Want to use Herbert Wilf's snake oil method to show $\sum_k \binom{2n+1}{2k}\binom{m+k}{2n} = \binom{2m+1}{2n}$

Published on 05 May 2026 - 22:04

score 376 · Answer 7 · 2026-05-10 09:58:42

376

Views

Young Tableaux generating function

Published on 10 May 2026 - 9:58

score 736 · Answer 8 · 2026-05-05 16:32:01

736

Views

Generating function of the sequence $\binom{2n}{n}^3H_n$

Published on 05 May 2026 - 16:32

score 50 · Answer 9 · 2026-05-04 22:22:13

50

Views

Expansion of fibonacci generating function

Published on 04 May 2026 - 22:22

score 114 · Answer 10 · 2026-05-05 20:06:34

114

Views

Partial fraction of $A(x)=\frac{x^2+x+1}{(1-x)^3}$

Published on 05 May 2026 - 20:06

score 128 · Answer 11 · 2026-04-30 19:29:15

128

Views

Moment generating Function Problem

Published on 30 Apr 2026 - 19:29

score 1.4k · Answer 12 · 2026-05-10 11:38:26

1.4k

Views

Circular permutations with alike objects

Published on 10 May 2026 - 11:38

score 60 · Answer 13 · 2026-05-10 11:38:48

60

Views

Recurrence formula in generating functions

Published on 10 May 2026 - 11:38

score 89 · Answer 14 · 2026-05-06 10:02:57

89

Views

I need some advice on solving this summation

Published on 06 May 2026 - 10:02

score 50 · Answer 15 · 2026-05-10 11:37:53

50

Views

Question to generating function

Published on 10 May 2026 - 11:37

List Question

The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$

How to multiply generating functions with $x^n$ and $x^{5n}$ and $x^{2n}$

Relationship between the generating functions of sequences $(a_n),(b_n)$ given $b_n=\sum^n_{i=1}a_i$.

Double-exponential sum (maybe it telescopes?)

Solve recurrence equation: $a_{n}=(n-1)(a_{n-1}+a_{n-2})$

Want to use Herbert Wilf's snake oil method to show $\sum_k \binom{2n+1}{2k}\binom{m+k}{2n} = \binom{2m+1}{2n}$

Young Tableaux generating function

Generating function of the sequence $\binom{2n}{n}^3H_n$

Expansion of fibonacci generating function

Partial fraction of $A(x)=\frac{x^2+x+1}{(1-x)^3}$

Moment generating Function Problem

Circular permutations with alike objects

Recurrence formula in generating functions

I need some advice on solving this summation

Question to generating function

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