Question

Expectation of the sum of N Poisson r.v.

score 68 · Answer 1 · 2026-04-14 13:03:26

68

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Expectation of the sum of N Poisson r.v.

Published on 14 Apr 2026 - 13:03

score 105 · Answer 2 · 2026-03-26 08:03:18

105

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Coefficients in Faulhabers' sum $\sum n^{2m+1}, \ m=0,1,2...$

Published on 26 Mar 2026 - 8:03

score 57 · Answer 3 · 2026-05-10 15:00:15

57

Views

Degree of generating polynomial associated with two partitions

Published on 10 May 2026 - 15:00

score 710 · Answer 4 · 2026-05-10 14:45:25

710

Views

Generating function for the Catalan numbers

Published on 10 May 2026 - 14:45

score 333 · Answer 5 · 2026-04-09 20:40:47

333

Views

Manipulation of generating functions+quadratic equation with generating functions

Published on 09 Apr 2026 - 20:40

score 22 · Answer 6 · 2026-05-11 03:17:29

22

Views

If $i$ is recurrent then expected recurrence time is the limit of $\frac 1 {(1-s)p_{ii}(s)}$

Published on 11 May 2026 - 3:17

score 103 · Answer 7 · 2026-04-14 11:36:50

103

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How to find recurrence for $f(x)$ coefficient in the expression $f(x)\cdot(1+2x+2x^2+x^3)=\frac{1}{1-x^3}$ using generating functions?

Published on 14 Apr 2026 - 11:36

score 59 · Answer 8 · 2026-04-12 12:10:19

59

Views

How many solutions are to the equation if there's range restriction on some numbers while some numbers must be divisible by $3$?

Published on 12 Apr 2026 - 12:10

score 133 · Answer 9 · 2026-04-13 09:21:35

133

Views

A better way to solve non-homogeneous linear recurrences?

Published on 13 Apr 2026 - 9:21

score 63 · Answer 10 · 2026-04-12 04:28:37

63

Views

How to solve multiplication of $3$ generating functions?

Published on 12 Apr 2026 - 4:28

score 87 · Answer 11 · 2026-04-16 19:29:01

87

Views

How to prove that generating function of series ($1 ,\binom{m}{1},\binom{m+1}{2},\binom{m+2}{3},...$ ) equals $\frac{1}{(1-z)^m}$ .

Published on 16 Apr 2026 - 19:29

score 89 · Answer 12 · 2026-04-14 15:42:53

89

Views

Connection between two solutions to the coin flipping pattern problem

Published on 14 Apr 2026 - 15:42

score 51 · Answer 13 · 2026-04-11 03:02:19

51

Views

Generating function from a summation relation

Published on 11 Apr 2026 - 3:02

score 42 · Answer 14 · 2026-05-10 15:10:25

42

Views

Find a polynomial $p(x)$ such that $p(x)(2x+6x^2+\cdots + n(n+1)x^n + \cdots ) = \frac{2x(1+x)^2}{(1-x)}$

Published on 10 May 2026 - 15:10

score 88 · Answer 15 · 2026-05-10 17:16:14

88

Views

Prove that $p_2(n) = \left \lfloor{\frac{n}{2}}\right \rfloor+1$ using identity

Published on 10 May 2026 - 17:16

List Question

Expectation of the sum of N Poisson r.v.

Coefficients in Faulhabers' sum $\sum n^{2m+1}, \ m=0,1,2...$

Degree of generating polynomial associated with two partitions

Generating function for the Catalan numbers

Manipulation of generating functions+quadratic equation with generating functions

If $i$ is recurrent then expected recurrence time is the limit of $\frac 1 {(1-s)p_{ii}(s)}$

How to find recurrence for $f(x)$ coefficient in the expression $f(x)\cdot(1+2x+2x^2+x^3)=\frac{1}{1-x^3}$ using generating functions?

How many solutions are to the equation if there's range restriction on some numbers while some numbers must be divisible by $3$?

A better way to solve non-homogeneous linear recurrences?

How to solve multiplication of $3$ generating functions?

How to prove that generating function of series ($1 ,\binom{m}{1},\binom{m+1}{2},\binom{m+2}{3},...$ ) equals $\frac{1}{(1-z)^m}$ .

Connection between two solutions to the coin flipping pattern problem

Generating function from a summation relation

Find a polynomial $p(x)$ such that $p(x)(2x+6x^2+\cdots + n(n+1)x^n + \cdots ) = \frac{2x(1+x)^2}{(1-x)}$

Prove that $p_2(n) = \left \lfloor{\frac{n}{2}}\right \rfloor+1$ using identity

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