Question

Finding EGF of $c(n,k)$: How did my professor manipulate $(\sum_{n \geq1} \frac{x^n}{n})^k$ into this nested summation?

score 54 · Answer 1 · 2023-11-18 10:15:59

54

Views

Finding EGF of $c(n,k)$: How did my professor manipulate $(\sum_{n \geq1} \frac{x^n}{n})^k$ into this nested summation?

Published on 18 Nov 2023 - 10:15

score 99 · Answer 2 · 2026-03-28 15:12:25

99

Views

Generating function of number of partitions of $n$ into parts at most $k$

Published on 28 Mar 2026 - 15:12

score 42 · Answer 3 · 2026-03-28 15:12:26

42

Views

Generating function of number of partitions of $n$ into all distinct parts

Published on 28 Mar 2026 - 15:12

score 180 · Answer 4 · 2026-03-26 21:25:46

180

Views

Seeking more alternate proofs of a combinatorial generating function identity $G(x)=\overline{G}(-x)^{-1}$ related to counting strings.

Published on 26 Mar 2026 - 21:25

score 45 · Answer 5 · 2023-11-20 11:10:30

45

Views

The generating function of sequence $a_n$ is known. How to evaluate the number (or density) of term "0" in $\{a_n\}$?

Published on 20 Nov 2023 - 11:10

score 481 · Answer 6 · 2023-11-20 16:48:34

481

Views

Some identities for polynomials defined by their generating function.

Published on 20 Nov 2023 - 16:48

score 67 · Answer 7 · 2026-03-26 16:06:04

67

Views

Making sense of generating functions in terms of the shift operator

Published on 26 Mar 2026 - 16:06

score 426 · Answer 8 · 2026-03-26 12:37:15

426

Views

Ramanujan-Type Harmonic Series $\sum_{r=0}^{\infty}\binom{2r}{r}^3\left(\frac{1/6+r}{2^{8r}}\right)H_{r-1/2}=-\frac{8\ln2}{9\pi}$

Published on 26 Mar 2026 - 12:37

score 60 · Answer 9 · 2023-11-27 16:52:28

60

Views

Simplifying Function into Generating Series

Published on 27 Nov 2023 - 16:52

score 85 · Answer 10 · 2026-03-25 12:47:28

85

Views

Stirling Numbers Exponential Generating Function Induction

Published on 25 Mar 2026 - 12:47

score 23 · Answer 11 · 2023-11-28 18:44:09

23

Views

Riordan array inversion, what goes wrong here

Published on 28 Nov 2023 - 18:44

score 225 · Answer 12 · 2026-04-02 13:25:21

225

Views

Functional equation: $f(z) = \sum_{n=0}^{\infty} f(n)^2 z^n$?

Published on 02 Apr 2026 - 13:25

score 35 · Answer 13 · 2023-11-29 22:28:25

35

Views

Applying log on a generating function

Published on 29 Nov 2023 - 22:28

score 129 · Answer 14 · 2026-03-26 22:18:19

129

Views

$g(z) = \sum_{n=0}^{\infty} \frac{g(n)}{(n+1)!} z^n$ with $0 \leq g(n)$?

Published on 26 Mar 2026 - 22:18

score 85 · Answer 15 · 2023-12-01 00:36:10

85

Views

How to prove $\sum^{m}_{k=0}(-2)^k\binom{2n-k}{n}\binom{m}{k}=0$ for $m=1,3,5,\dots,2n-1$?

Published on 01 Dec 2023 - 0:36

List Question

Finding EGF of $c(n,k)$: How did my professor manipulate $(\sum_{n \geq1} \frac{x^n}{n})^k$ into this nested summation?

Generating function of number of partitions of $n$ into parts at most $k$

Generating function of number of partitions of $n$ into all distinct parts

Seeking more alternate proofs of a combinatorial generating function identity $G(x)=\overline{G}(-x)^{-1}$ related to counting strings.

The generating function of sequence $a_n$ is known. How to evaluate the number (or density) of term "0" in $\{a_n\}$?

Some identities for polynomials defined by their generating function.

Making sense of generating functions in terms of the shift operator

Ramanujan-Type Harmonic Series $\sum_{r=0}^{\infty}\binom{2r}{r}^3\left(\frac{1/6+r}{2^{8r}}\right)H_{r-1/2}=-\frac{8\ln2}{9\pi}$

Simplifying Function into Generating Series

Stirling Numbers Exponential Generating Function Induction

Riordan array inversion, what goes wrong here

Functional equation: $f(z) = \sum_{n=0}^{\infty} f(n)^2 z^n$?

Applying log on a generating function

$g(z) = \sum_{n=0}^{\infty} \frac{g(n)}{(n+1)!} z^n$ with $0 \leq g(n)$?

How to prove $\sum^{m}_{k=0}(-2)^k\binom{2n-k}{n}\binom{m}{k}=0$ for $m=1,3,5,\dots,2n-1$?

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