Question

Reverse generating function for $a_n = (-1)^n C_{2n}^n 4^{-n}$

score 87 · Answer 1 · 2026-04-16 05:02:38

87

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Reverse generating function for $a_n = (-1)^n C_{2n}^n 4^{-n}$

Published on 16 Apr 2026 - 5:02

score 130 · Answer 2 · 2026-04-16 00:20:11

130

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Solve the following recurrence $\left(n+1\right)a_n=na_{n-1}+1\:\:\:\:\:\forall n\ge 1\:and\:a_0\:=\:1$

Published on 16 Apr 2026 - 0:20

score 118 · Answer 3 · 2026-04-14 13:35:53

118

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Arranging $120$ students into $6$ different groups so that the largest and smallest group differ by $2$ members

Published on 14 Apr 2026 - 13:35

score 277 · Answer 4 · 2026-04-13 18:33:36

277

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Generating function for length of coin tosses until 5 consecutive heads

Published on 13 Apr 2026 - 18:33

score 66 · Answer 5 · 2026-04-20 03:17:31

66

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Show that $J_0(x) + 2\sum_{n = 1}^\infty J_{2n}(x) = 1$

Published on 20 Apr 2026 - 3:17

score 53 · Answer 6 · 2026-03-25 22:06:24

53

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Property of the symmetric reduction of a multivariate polynomial

Published on 25 Mar 2026 - 22:06

score 66 · Answer 7 · 2026-04-12 15:17:49

66

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For what sequence is $A(x^{2})$ a generating function?

Published on 12 Apr 2026 - 15:17

score 169 · Answer 8 · 2026-04-25 15:47:10

169

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Solving infinite ladder of differential equations using generating functions.

Published on 25 Apr 2026 - 15:47

score 27 · Answer 9 · 2026-04-08 18:29:04

27

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How to find limits of probabilities using generating functions of markov chain?

Published on 08 Apr 2026 - 18:29

score 249 · Answer 10 · 2026-04-16 17:34:20

249

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The number of edges in the $k$-dimensional cube $Q_k$ can be found by the recurrence relation: $e(Q_1)=1$; $e(Q_n)=2e(Q_{n-1})+2^{n-1}$ for $n\ge 2$

Published on 16 Apr 2026 - 17:34

score 337 · Answer 11 · 2026-04-16 23:32:07

337

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Find the generating function of the sequence $(a_0, a_1, a_2, \dots)$ where $a_n = n2^n$

Published on 16 Apr 2026 - 23:32

score 48 · Answer 12 · 2026-04-11 09:32:55

48

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Finding a generating function involving two sets of objects.

Published on 11 Apr 2026 - 9:32

score 426 · Answer 13 · 2026-04-12 16:54:14

426

Views

Find closed formula for the exponential generating function of sequence counting permutations with 2 cycles.

Published on 12 Apr 2026 - 16:54

score 54 · Answer 14 · 2026-04-13 06:11:12

54

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A simple and more generalised way to define this coefficient

Published on 13 Apr 2026 - 6:11

score 97 · Answer 15 · 2026-04-14 20:51:03

97

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Evaluating $S_{N} = \sum_{i=0}^\infty \frac{i^N}{4^i}$ using recursion

Published on 14 Apr 2026 - 20:51

List Question

Reverse generating function for $a_n = (-1)^n C_{2n}^n 4^{-n}$

Solve the following recurrence $\left(n+1\right)a_n=na_{n-1}+1\:\:\:\:\:\forall n\ge 1\:and\:a_0\:=\:1$

Arranging $120$ students into $6$ different groups so that the largest and smallest group differ by $2$ members

Generating function for length of coin tosses until 5 consecutive heads

Show that $J_0(x) + 2\sum_{n = 1}^\infty J_{2n}(x) = 1$

Property of the symmetric reduction of a multivariate polynomial

For what sequence is $A(x^{2})$ a generating function?

Solving infinite ladder of differential equations using generating functions.

How to find limits of probabilities using generating functions of markov chain?

The number of edges in the $k$-dimensional cube $Q_k$ can be found by the recurrence relation: $e(Q_1)=1$; $e(Q_n)=2e(Q_{n-1})+2^{n-1}$ for $n\ge 2$

Find the generating function of the sequence $(a_0, a_1, a_2, \dots)$ where $a_n = n2^n$

Finding a generating function involving two sets of objects.

Find closed formula for the exponential generating function of sequence counting permutations with 2 cycles.

A simple and more generalised way to define this coefficient

Evaluating $S_{N} = \sum_{i=0}^\infty \frac{i^N}{4^i}$ using recursion

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