List questions from generating-functions

Published on 08 Jun 2020 - 21:00

272

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Combinatorial interpretation of the identity $(f \circ f \circ f)(x) = x$ where $f(x) = 1/(1-x)$ for $x\in(-1,1)$

Published on 26 Mar 2026 - 2:56

49

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Show that $F(x)=\frac{x}{(1-x)^2}-\frac{2x}{(2-x)^2}=\sum_{n=0}^{\infty}n(1-2^{-n})x^n$

Published on 10 Jun 2020 - 14:40

233

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Question about product of generating functions in a proof that for positive integer $n$, $\sum_{k=0}^n(-1)^k\binom nk\binom{2n-k}n=1$.

Published on 10 Jun 2020 - 20:35

297

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A conjectured criterion for a generalized ramanujan tau function

Published on 25 Mar 2026 - 20:41

148

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Combinatorics - Generating function problem

Published on 25 Mar 2026 - 2:57

41

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Series from $1,2,3,4$ that sum to $n$

Published on 11 Jun 2020 - 14:04

148

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Elegant check of equalities in a 3Blue1Brown post on the Leibniz formula?

Published on 13 Jun 2020 - 3:34

73

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Exponential generating function wilf 3.12

Published on 14 Jun 2020 - 1:32

85

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Solve for $a_{n}$ where $a_{n} = 4a_{n-1} + 2^{2n-1}$, $a_0=1$ and $a_1=6$ .

Published on 30 Mar 2026 - 13:25

80

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How to express this combination as a formula?

Published on 15 Jun 2020 - 7:42

147

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Dyck type lattice paths bounded between the lines $y=x$ and $y=x+k$

Published on 15 Jun 2020 - 12:03

28

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How does one handle series generating functions with multiple equals signs?

Published on 27 Mar 2026 - 20:12

67

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What is the solution to this recurrence given that $f(z)$ is an exponential generating function

Published on 17 Jun 2020 - 10:01

89

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Generating function of recursive algorithm with random subcalls

Published on 25 Mar 2026 - 17:35

List Question

Find $a(n)$ with generating functions

Combinatorial interpretation of the identity $(f \circ f \circ f)(x) = x$ where $f(x) = 1/(1-x)$ for $x\in(-1,1)$

Show that $F(x)=\frac{x}{(1-x)^2}-\frac{2x}{(2-x)^2}=\sum_{n=0}^{\infty}n(1-2^{-n})x^n$

Question about product of generating functions in a proof that for positive integer $n$, $\sum_{k=0}^n(-1)^k\binom nk\binom{2n-k}n=1$.

A conjectured criterion for a generalized ramanujan tau function

Combinatorics - Generating function problem

Series from $1,2,3,4$ that sum to $n$

Elegant check of equalities in a 3Blue1Brown post on the Leibniz formula?

Exponential generating function wilf 3.12

Solve for $a_{n}$ where $a_{n} = 4a_{n-1} + 2^{2n-1}$, $a_0=1$ and $a_1=6$ .

How to express this combination as a formula?

Dyck type lattice paths bounded between the lines $y=x$ and $y=x+k$

How does one handle series generating functions with multiple equals signs?

What is the solution to this recurrence given that $f(z)$ is an exponential generating function

Generating function of recursive algorithm with random subcalls

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