Question

Generating function for partitions into parts

score 174 · Answer 1 · 2026-03-25 06:17:58

174

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Generating function for partitions into parts

Published on 25 Mar 2026 - 6:17

score 91 · Answer 2 · 2018-02-26 22:53:37

91

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$Pr(A+B+C=X+Y+Z)$ with $A, B, C, X, Y, Z$ being iid random variables

Published on 26 Feb 2018 - 22:53

score 60 · Answer 3 · 2018-02-26 23:37:07

60

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$x_1, x_2, x_3, x_4,\ldots,x_k$ being random signs that are independent |-> $\operatorname{Var}(\sum_{k=1}^n b_k x_k) = \sum_{k=1}^n {b_k}^2$

Published on 26 Feb 2018 - 23:37

score 238 · Answer 4 · 2026-03-20 11:37:22

238

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extracting Catalan numbers from its generating function (binomial theorem)

Published on 20 Mar 2026 - 11:37

score 121 · Answer 5 · 2018-02-28 13:56:14

What is the generating function for $(a_n)_{0\leq n}$, where $a_n$ is defined as $a_0 = 0$ and $a_{n+1} = a_n + (n+1)^3$ for all $n\geq0$?

score 700 · Answer 6 · 2026-03-25 06:22:52

700

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Let $p_3(n)$ be the number of partitions of $n$ into parts that are not multiples of 3. What is the generating function for the sequence $\{p_3(n)\}$

Published on 25 Mar 2026 - 6:22

score 85 · Answer 7 · 2026-03-25 06:12:53

85

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Derivation of an inequality regarding absolute moments and MGF

Published on 25 Mar 2026 - 6:12

score 504 · Answer 8 · 2018-03-02 01:24:15

504

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Find the explicit formula for the numbers $a_n$

Published on 02 Mar 2018 - 1:24

score 167 · Answer 9 · 2018-03-02 06:35:07

167

Views

A problem of combinatorics (reduced from a problem of computing probability generating function)

Published on 02 Mar 2018 - 6:35

score 528 · Answer 10 · 2018-03-04 10:04:55

528

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Generating function, N coin tosses: Find the probability that the total number of heads is a) even b) divisible by 3.

Published on 04 Mar 2018 - 10:04

score 193 · Answer 11 · 2026-03-25 06:16:15

193

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Is there a generating function for this sequence?

Published on 25 Mar 2026 - 6:16

score 149 · Answer 12 · 2026-03-17 00:55:35

149

Views

Proof verification : Inequality involving moment generating function (MGF)

Published on 17 Mar 2026 - 0:55

score 120 · Answer 13 · 2018-03-06 23:13:36

120

Views

Verifying Newton's Binomial Series for $(1+x)^{−2}$

Published on 06 Mar 2018 - 23:13

score 1k · Answer 14 · 2018-03-07 12:28:48

1k

Views

Looking for a closed form solution $P_{n+2}(x)=x^2 P'_{n+1}(x)+(n+1)xP_{n+1}(x)-(n+1)P'_n(x) $

Published on 07 Mar 2018 - 12:28

score 138 · Answer 15 · 2026-03-24 08:42:02

138

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Magic sum with binomial coefficient

Published on 24 Mar 2026 - 8:42

List Question

Generating function for partitions into parts

$Pr(A+B+C=X+Y+Z)$ with $A, B, C, X, Y, Z$ being iid random variables

$x_1, x_2, x_3, x_4,\ldots,x_k$ being random signs that are independent |-> $\operatorname{Var}(\sum_{k=1}^n b_k x_k) = \sum_{k=1}^n {b_k}^2$

extracting Catalan numbers from its generating function (binomial theorem)

What is the generating function for $(a_n)_{0\leq n}$, where $a_n$ is defined as $a_0 = 0$ and $a_{n+1} = a_n + (n+1)^3$ for all $n\geq0$?

Let $p_3(n)$ be the number of partitions of $n$ into parts that are not multiples of 3. What is the generating function for the sequence $\{p_3(n)\}$

Derivation of an inequality regarding absolute moments and MGF

Find the explicit formula for the numbers $a_n$

A problem of combinatorics (reduced from a problem of computing probability generating function)

Generating function, N coin tosses: Find the probability that the total number of heads is a) even b) divisible by 3.

Is there a generating function for this sequence?

Proof verification : Inequality involving moment generating function (MGF)

Verifying Newton's Binomial Series for $(1+x)^{−2}$

Looking for a closed form solution $P_{n+2}(x)=x^2 P'_{n+1}(x)+(n+1)xP_{n+1}(x)-(n+1)P'_n(x) $

Magic sum with binomial coefficient

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