List questions from generating-functions

Published on 24 Nov 2015 - 16:16

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generating functions (recurrence relations)

Published on 24 Nov 2015 - 19:05

1.1k

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Determine the number of all nonnegative integer solutions to $x + y + z = 11$ with $x\leq 3$, $y\leq 4$, and $z \leq 6$.

Published on 26 Nov 2015 - 0:28

38

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Need some hints for generating function-assignment.

Published on 26 Nov 2015 - 13:17

142

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Find the generating function for given series

Published on 26 Nov 2015 - 14:18

609

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Prove all numbers in a sequence are perfect squares

Published on 27 Nov 2015 - 16:09

168

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Find generating function of sequences: $a_n=(n^2+n+1)_{n\ge0},b_n=(2^{1+[\frac{n}{3}]})_{n\ge 0}$

Published on 28 Nov 2015 - 19:03

3.1k

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How to get nth derivative of $\arcsin x$

Published on 03 Apr 2026 - 14:27

1.1k

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Exponential generating function and number of balls

Published on 29 Nov 2015 - 10:37

90

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Why is the Taylor series of $1/\sqrt{1-4q^2}$ popping up in my recursively defined triangle of polynomials?

Published on 29 Nov 2015 - 23:03

200

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Impossible counting problem with Generating function

Published on 01 Dec 2015 - 2:08

131

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Another combinatorial identity of McKay

Published on 01 Dec 2015 - 5:00

36

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Combinatorics partitioning problem: find $\sum_{n\geq 0} a_{n,k}\frac{x^n}{n!}$

Published on 01 Dec 2015 - 5:25

9.1k

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Prove the generating function for the Catalan number sequence is $f(x) = \frac{1 -\sqrt{1-4x}}{2x}$

Published on 28 Mar 2026 - 20:58

391

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Finding the coefficient of x^n generating functions

Published on 02 Dec 2015 - 5:02

List Question

Find closed form of a sequence $2,5,11,23,...$

generating functions (recurrence relations)

Determine the number of all nonnegative integer solutions to $x + y + z = 11$ with $x\leq 3$, $y\leq 4$, and $z \leq 6$.

Need some hints for generating function-assignment.

Find the generating function for given series

Prove all numbers in a sequence are perfect squares

Find generating function of sequences: $a_n=(n^2+n+1)_{n\ge0},b_n=(2^{1+[\frac{n}{3}]})_{n\ge 0}$

How to get nth derivative of $\arcsin x$

Exponential generating function and number of balls

Why is the Taylor series of $1/\sqrt{1-4q^2}$ popping up in my recursively defined triangle of polynomials?

Impossible counting problem with Generating function

Another combinatorial identity of McKay

Combinatorics partitioning problem: find $\sum_{n\geq 0} a_{n,k}\frac{x^n}{n!}$

Prove the generating function for the Catalan number sequence is $f(x) = \frac{1 -\sqrt{1-4x}}{2x}$

Finding the coefficient of x^n generating functions

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