List questions from generating-functions

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Find a closed form for $\sum_{k=0}^{n} k^3$

Published on 28 Mar 2026 - 0:30

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Extracting a coefficient from a generating function

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Probability Generating Functions with Three Dice

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Find a generating function for $\sum_{k=0}^{n} k^2$

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How many ways you can make change for an amount N using A and B monets.

Published on 14 Jun 2014 - 14:00

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Prove equilvalence of generating series with compositions.

Published on 14 Jun 2014 - 21:27

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Combinatorics: Binary Strings

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Generating function for picking j balls without replacement from an urn

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Solve linear homogeneous recurrent relation with constant coef using generating functions

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Generating Function for the number of ways representing positive integer with odd numbers

Published on 21 Jun 2014 - 19:59

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Products of n exponential generating functions

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The number of permutations of $\{1,2,\ldots,n\}$ that have exactly one ascent (rise).

Published on 26 Jun 2014 - 13:50

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Asymptotic approximation for the r-associated Stirling numbers of the second kind

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A bijection defined on the set of configuration of lamps

Published on 28 Jun 2014 - 15:32

List Question

How to simplify $F(x)=\sum_{n}^{\infty}\sum_{k}^{\infty}{n-k-1\choose k}x^n$?

Find a closed form for $\sum_{k=0}^{n} k^3$

Extracting a coefficient from a generating function

Probability Generating Functions with Three Dice

Find a generating function for $\sum_{k=0}^{n} k^2$

How many ways you can make change for an amount N using A and B monets.

Prove equilvalence of generating series with compositions.

Combinatorics: Binary Strings

Generating function for picking j balls without replacement from an urn

Solve linear homogeneous recurrent relation with constant coef using generating functions

Generating Function for the number of ways representing positive integer with odd numbers

Products of n exponential generating functions

The number of permutations of $\{1,2,\ldots,n\}$ that have exactly one ascent (rise).

Asymptotic approximation for the r-associated Stirling numbers of the second kind

A bijection defined on the set of configuration of lamps

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