Question

Exponential Generating Function for the recurrence relation $a_n=\sum_{k=1}^n {n\choose k}a_{n-k}$

score 127 · Answer 1 · 2026-04-16 15:46:59

127

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Exponential Generating Function for the recurrence relation $a_n=\sum_{k=1}^n {n\choose k}a_{n-k}$

Published on 16 Apr 2026 - 15:46

score 35 · Answer 2 · 2026-04-12 13:24:39

35

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Find $a_0$ and $a_1$ when given a generating function.

Published on 12 Apr 2026 - 13:24

score 70 · Answer 3 · 2026-04-16 09:10:03

Finding Exponents of Generating Function $A(x)=\prod\limits_{k=1}^{\infty}\frac{1-x^{6k}}{(1-x^{2k})(1-x^{3k})} $

score 227 · Answer 4 · 2026-04-15 06:42:46

227

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Generating function for distributing $k$ indistinguishable elements into $n$ distinguishable bins such that each bin has even number of elements.

Published on 15 Apr 2026 - 6:42

score 45 · Answer 5 · 2026-04-12 20:02:53

45

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Number of partitions of $n$ in which parts can occur at most 7 times

Published on 12 Apr 2026 - 20:02

score 50 · Answer 6 · 2026-04-14 11:24:27

50

Views

Semi-Complicated recurrence relation to be solved via generating functions

Published on 14 Apr 2026 - 11:24

score 176 · Answer 7 · 2026-04-17 10:07:43

176

Views

$\binom{n - 1 + k}{k}$ as the basis for a polynomial vector space, and the use of $\frac{1}{(1-x)^n}$ to derive generating functions for $a_n = n^k$

Published on 17 Apr 2026 - 10:07

score 40 · Answer 8 · 2026-04-14 22:57:11

40

Views

generating functions as jet bundles

Published on 14 Apr 2026 - 22:57

score 199 · Answer 9 · 2026-04-15 00:44:21

199

Views

Combinatorial proof of $\sum_{i=0}^m{\binom{x+y+i}{i} \binom{y}{a-i} \binom{x}{b-i} }=\binom{x+a}{b} \binom{y+b}{a}$

Published on 15 Apr 2026 - 0:44

score 191 · Answer 10 · 2026-04-09 10:08:33

191

Views

Use probability generating function to calculate probability

Published on 09 Apr 2026 - 10:08

score 292 · Answer 11 · 2026-04-09 10:20:35

292

Views

Forward difference of Bernoulli polynomials

Published on 09 Apr 2026 - 10:20

score 59 · Answer 12 · 2026-04-17 00:30:59

59

Views

Does $\prod_k (x - r_k)^{m_k} = \prod_k (1 - \frac{x}{r_k})^{m_k}$?

Published on 17 Apr 2026 - 0:30

score 437 · Answer 13 · 2026-04-08 17:43:07

437

Views

The coefficient and asymptotic in generating function

Published on 08 Apr 2026 - 17:43

score 440 · Answer 14 · 2026-04-16 01:31:16

440

Views

Coefficient of $\frac{1}{1-x-x^2-..-x^{d-1}}$ and its asymptotic

Published on 16 Apr 2026 - 1:31

score 82 · Answer 15 · 2026-04-14 23:58:48

82

Views

A $\zeta$-like sum of the positive roots of $\csc x=x$.

Published on 14 Apr 2026 - 23:58

List Question

Exponential Generating Function for the recurrence relation $a_n=\sum_{k=1}^n {n\choose k}a_{n-k}$

Find $a_0$ and $a_1$ when given a generating function.

Finding Exponents of Generating Function $A(x)=\prod\limits_{k=1}^{\infty}\frac{1-x^{6k}}{(1-x^{2k})(1-x^{3k})} $

Generating function for distributing $k$ indistinguishable elements into $n$ distinguishable bins such that each bin has even number of elements.

Number of partitions of $n$ in which parts can occur at most 7 times

Semi-Complicated recurrence relation to be solved via generating functions

$\binom{n - 1 + k}{k}$ as the basis for a polynomial vector space, and the use of $\frac{1}{(1-x)^n}$ to derive generating functions for $a_n = n^k$

generating functions as jet bundles

Combinatorial proof of $\sum_{i=0}^m{\binom{x+y+i}{i} \binom{y}{a-i} \binom{x}{b-i} }=\binom{x+a}{b} \binom{y+b}{a}$

Use probability generating function to calculate probability

Forward difference of Bernoulli polynomials

Does $\prod_k (x - r_k)^{m_k} = \prod_k (1 - \frac{x}{r_k})^{m_k}$?

The coefficient and asymptotic in generating function

Coefficient of $\frac{1}{1-x-x^2-..-x^{d-1}}$ and its asymptotic

A $\zeta$-like sum of the positive roots of $\csc x=x$.

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