List questions from generating-functions

Published on 20 Oct 2016 - 12:44

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Give the generating function for the number of partitions of an integer into parts of size one through ten

Published on 21 Oct 2016 - 4:41

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Assume that $(a_n)^{\infty}_{n=0}$ is a sequence given by $a_0=1$ and $a_{n+1}=2a_{n}+n$ for all $n \ge 0$, what is the formula for $a_n$?

Published on 22 Oct 2016 - 1:48

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Find the sum $\sum_{n=2}^{\infty} \frac{\binom n2}{4^n} = \frac{\binom 22}{16}+\frac{\binom 32}{64}+\frac{\binom 42}{256}+\cdots$.

Published on 25 Oct 2016 - 22:13

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Generating function

Published on 25 Mar 2026 - 20:40

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Find the number of solutions?

Published on 27 Oct 2016 - 9:01

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Generating function of Hadamard product of two power series

Published on 27 Oct 2016 - 13:59

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harmonic series - generating function

Published on 28 Oct 2016 - 16:06

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Find coefficient of ordinary generating function

Published on 31 Oct 2016 - 0:10

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Find the generating function for the number of solutions

Published on 31 Oct 2016 - 3:48

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Partition Proving

Published on 27 Mar 2026 - 23:38

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How to identify the coefficient of $x^k$ in $1/(1-x)^N$ where $N$ can be a large integer

Published on 03 Nov 2016 - 16:29

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Counting the number of ways three dice can sum to $n$

Published on 04 Nov 2016 - 21:34

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Inverse of a symmetric tridiagonal almost-Toeplitz matrix

Published on 25 Mar 2026 - 6:50

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Compositions and Partitions

Published on 27 Mar 2026 - 23:30

List Question

Simplify or find a lower bound

Give the generating function for the number of partitions of an integer into parts of size one through ten

Assume that $(a_n)^{\infty}_{n=0}$ is a sequence given by $a_0=1$ and $a_{n+1}=2a_{n}+n$ for all $n \ge 0$, what is the formula for $a_n$?

Find the sum $\sum_{n=2}^{\infty} \frac{\binom n2}{4^n} = \frac{\binom 22}{16}+\frac{\binom 32}{64}+\frac{\binom 42}{256}+\cdots$.

Generating function

Find the number of solutions?

Generating function of Hadamard product of two power series

harmonic series - generating function

Find coefficient of ordinary generating function

Find the generating function for the number of solutions

Partition Proving

How to identify the coefficient of $x^k$ in $1/(1-x)^N$ where $N$ can be a large integer

Counting the number of ways three dice can sum to $n$

Inverse of a symmetric tridiagonal almost-Toeplitz matrix

Compositions and Partitions

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