Question

Writing $1+3x^2+8x^4+21x^6+\cdots$ as a power series representation

score 143 · Answer 1 · 2026-03-28 08:09:29

143

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Writing $1+3x^2+8x^4+21x^6+\cdots$ as a power series representation

Published on 28 Mar 2026 - 8:09

score 157 · Answer 2 · 2014-12-21 00:50:40

157

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How to write $1-x-x^3+x^4+x^5+x^6-x^7 \cdots$ as a power series representation

Published on 21 Dec 2014 - 0:50

score 134 · Answer 3 · 2014-12-21 02:02:47

134

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Series expansion of $\frac{1}{(1+x)(1−x)(1+x^2)(1−x^2)(1+x^3)(1−x^3)\cdots}$?

Published on 21 Dec 2014 - 2:02

score 94 · Answer 4 · 2026-03-27 00:55:18

94

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Truncation of partitions generating function question

Published on 27 Mar 2026 - 0:55

score 81 · Answer 5 · 2026-03-29 10:08:54

81

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What happens from $ (1+(x+x^2))^n$ to $\sum_k {n \choose k} (x+x^2)^n$?

Published on 29 Mar 2026 - 10:08

score 266 · Answer 6 · 2026-03-25 23:38:27

266

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Expansion for r-associated Stirling numbers of the second kind

Published on 25 Mar 2026 - 23:38

score 264 · Answer 7 · 2026-03-28 18:13:31

264

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What is the convolution here?

Published on 28 Mar 2026 - 18:13

score 102 · Answer 8 · 2014-12-26 21:50:09

What is the generating function to calculate the number of functions $f:\{1,2,3,4,5,6,7,8,9,10\}\to\{1,2,3,4,5,6,7\}$ with $|Im(f)|=4$?

score 66 · Answer 9 · 2014-12-28 04:43:53

66

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the coefficient of $t^{18}$ in $t^6(1+t+\cdots+t^5)^6 $ equals the coefficient of $t^{12}$ in $(1+t+\cdots+t^5)^6 $.

Published on 28 Dec 2014 - 4:43

score 985 · Answer 10 · 2026-03-26 02:57:50

985

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How many ways to visit 4 cities so that each city is visited exactly 4 times without visiting the same city twice in a row?

Published on 26 Mar 2026 - 2:57

score 84 · Answer 11 · 2026-03-30 03:34:16

84

Views

Closed form for generating function of Riemann Xi function

Published on 30 Mar 2026 - 3:34

score 84 · Answer 12 · 2014-12-30 03:32:33

84

Views

If $X \sim Bin(n,p)$, using $E(X(X-1)) = g''(1) = n(n-1)p^2$ show that Var$(X) = npg$.

Published on 30 Dec 2014 - 3:32

score 113 · Answer 13 · 2026-03-25 16:02:23

113

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Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?

Published on 25 Mar 2026 - 16:02

score 94 · Answer 14 · 2015-01-01 11:48:30

94

Views

Determine sequence using generating function.

Published on 01 Jan 2015 - 11:48

score 270 · Answer 15 · 2015-01-01 21:00:56

270

Views

Recursion with generating function.

Published on 01 Jan 2015 - 21:00

List Question

Writing $1+3x^2+8x^4+21x^6+\cdots$ as a power series representation

How to write $1-x-x^3+x^4+x^5+x^6-x^7 \cdots$ as a power series representation

Series expansion of $\frac{1}{(1+x)(1−x)(1+x^2)(1−x^2)(1+x^3)(1−x^3)\cdots}$?

Truncation of partitions generating function question

What happens from $ (1+(x+x^2))^n$ to $\sum_k {n \choose k} (x+x^2)^n$?

Expansion for r-associated Stirling numbers of the second kind

What is the convolution here?

What is the generating function to calculate the number of functions $f:\{1,2,3,4,5,6,7,8,9,10\}\to\{1,2,3,4,5,6,7\}$ with $|Im(f)|=4$?

the coefficient of $t^{18}$ in $t^6(1+t+\cdots+t^5)^6 $ equals the coefficient of $t^{12}$ in $(1+t+\cdots+t^5)^6 $.

How many ways to visit 4 cities so that each city is visited exactly 4 times without visiting the same city twice in a row?

Closed form for generating function of Riemann Xi function

If $X \sim Bin(n,p)$, using $E(X(X-1)) = g''(1) = n(n-1)p^2$ show that Var$(X) = npg$.

Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?

Determine sequence using generating function.

Recursion with generating function.

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