List questions from generating-functions

Published on 20 Dec 2015 - 18:01

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Generating functions - deriving a formula for the sum $1^2 + 2^2 +\cdots+n^2$

Published on 21 Dec 2015 - 20:18

635

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Ordinary generating function of powers of 2

Published on 23 Dec 2015 - 22:01

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Closed form of a generating function $\sum _{n=1}^\infty x^{n^2}$

Published on 05 Apr 2026 - 23:42

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Derive the generating function: $\frac1{(1-x)^3}= \sum_{n=0}^\infty \binom{n+2}{2}x^n$

Published on 26 Dec 2015 - 20:13

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When the product of dice rolls yields a square

Published on 28 Dec 2015 - 22:50

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let $\mu$ = $E[V]$ where V is a typical family resulting from one individual, then prove that $E[X_n] = \mu^2$

Published on 31 Dec 2015 - 13:50

226

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What is the significance of this identity relating to partitions?

Published on 29 Mar 2026 - 14:07

32

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Mean value theorem applied to the numerator in the result of the generating function

Published on 02 Jan 2016 - 17:27

36

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Get the probability generating function of $X$ from $Y$

Published on 03 Jan 2016 - 11:02

214

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Combinatorics problem using generating functions 1

Published on 05 Jan 2016 - 18:34

97

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Combinatorics problem using generating exp functions 2

Published on 05 Jan 2016 - 18:37

47

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Is my generating function correct so far for this recurrence?

Published on 06 Jan 2016 - 4:59

275

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Derivation of Catalan numbers

Published on 29 Mar 2026 - 3:10

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Finding the expectation and variance from a probability generating function

Published on 02 Apr 2026 - 9:37

List Question

Infinite recurrence relation which depends on subsequent sequence values

Generating functions - deriving a formula for the sum $1^2 + 2^2 +\cdots+n^2$

Ordinary generating function of powers of 2

Closed form of a generating function $\sum _{n=1}^\infty x^{n^2}$

Derive the generating function: $\frac1{(1-x)^3}= \sum_{n=0}^\infty \binom{n+2}{2}x^n$

When the product of dice rolls yields a square

let $\mu$ = $E[V]$ where V is a typical family resulting from one individual, then prove that $E[X_n] = \mu^2$

What is the significance of this identity relating to partitions?

Mean value theorem applied to the numerator in the result of the generating function

Get the probability generating function of $X$ from $Y$

Combinatorics problem using generating functions 1

Combinatorics problem using generating exp functions 2

Is my generating function correct so far for this recurrence?

Derivation of Catalan numbers

Finding the expectation and variance from a probability generating function

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