List questions from generating-functions

Published on 26 Mar 2026 - 9:27

127

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How can I determine the sequence generated by this generating function: $B(x)=(x+3)^2 + \frac{x}{(1-3x)^6}$?

Published on 11 Feb 2019 - 9:20

778

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How to solve this recurrence relation using generating functions: $a_n = 10 a_{n-1}-25 a_{n-2} + 5^n\binom{n+2}2$?

Published on 11 Feb 2019 - 10:03

1k

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How to find the generator of the following ideals?

Published on 12 Feb 2019 - 11:10

294

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Finding the generating function of a sequence for $n$ pennies

Published on 12 Feb 2019 - 15:16

331

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Generating function for a special binary string

Published on 13 Feb 2019 - 7:20

53

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Find closed form of composition.

Published on 13 Feb 2019 - 19:11

236

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Find generating function of $ a_n=2a_{n-1}-3a_{n-2}+4n-1 $

Published on 14 Feb 2019 - 8:35

191

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Probability mass function from a generating function

Published on 14 Feb 2019 - 14:10

55

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How to construct a function with these hypotheses?

Published on 25 Mar 2026 - 23:15

206

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Number of $n$-permutations with $r$ inversions modulo $k$

Published on 20 Feb 2019 - 1:34

75

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Generating function problem with expectation.

Published on 20 Feb 2019 - 18:57

423

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Lattice Paths with moves $(1, 0)$, $(1, 1)$, and $(1, -1)$

Published on 20 Feb 2019 - 22:04

71

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What distribution has the probability generating function $\mathbb E[s^X]=\left(\frac{1-\delta P}{1-sP}\right)^{\frac{1-s}{\delta-s}}$?

Published on 21 Feb 2019 - 20:20

200

Views

Allan Gut Inter. Course on probability First Edition Chap 3 Problem 2

Published on 21 Feb 2019 - 22:47

List Question

Number of unlabeled rooted trees with n vertices and k leaves

How can I determine the sequence generated by this generating function: $B(x)=(x+3)^2 + \frac{x}{(1-3x)^6}$?

How to solve this recurrence relation using generating functions: $a_n = 10 a_{n-1}-25 a_{n-2} + 5^n\binom{n+2}2$?

How to find the generator of the following ideals?

Finding the generating function of a sequence for $n$ pennies

Generating function for a special binary string

Find closed form of composition.

Find generating function of $ a_n=2a_{n-1}-3a_{n-2}+4n-1 $

Probability mass function from a generating function

How to construct a function with these hypotheses?

Number of $n$-permutations with $r$ inversions modulo $k$

Generating function problem with expectation.

Lattice Paths with moves $(1, 0)$, $(1, 1)$, and $(1, -1)$

What distribution has the probability generating function $\mathbb E[s^X]=\left(\frac{1-\delta P}{1-sP}\right)^{\frac{1-s}{\delta-s}}$?

Allan Gut Inter. Course on probability First Edition Chap 3 Problem 2

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