Question

Solve the recursion $a_{n+1} = a_n\left(1+\frac{1}{n}\right) +1; a_1=1$

score 60 · Answer 1 · 2018-03-22 17:26:35

60

Views

Solve the recursion $a_{n+1} = a_n\left(1+\frac{1}{n}\right) +1; a_1=1$

Published on 22 Mar 2018 - 17:26

score 592 · Answer 2 · 2018-03-22 23:52:40

592

Views

What is the value of the second derivative of a probability generating function?

Published on 22 Mar 2018 - 23:52

score 42 · Answer 3 · 2026-03-25 04:17:33

42

Views

Set and Inequality, something like generating function.

Published on 25 Mar 2026 - 4:17

score 165 · Answer 4 · 2018-03-24 17:04:55

165

Views

Calculating the coefficient of $x^k$

Published on 24 Mar 2018 - 17:04

score 79 · Answer 5 · 2018-03-25 14:05:49

79

Views

Expectation and variance of 4th generation

Published on 25 Mar 2018 - 14:05

score 52 · Answer 6 · 2018-03-25 14:34:30

How does $(a_0+a_1x+a_2x^2+a_3x^3+\cdots)^k$ become $\sum_{n\geq 0}\big(\sum_{i_1+\cdots+i_k=n\\ i_{ij}\geq 0} a_{i_1}a_{i_2}\cdots a_{i_k}\big)x^n$?

score 70 · Answer 7 · 2018-03-25 17:22:53

70

Views

Create the generating function for this distribution problem.

Published on 25 Mar 2018 - 17:22

score 424 · Answer 8 · 2026-03-25 06:24:32

424

Views

How To Apply and Understand the Generating Function for Number Partitioning

Published on 25 Mar 2026 - 6:24

score 134 · Answer 9 · 2026-03-25 04:38:52

134

Views

N-th term of generating function of almost fibonacci sequence

Published on 25 Mar 2026 - 4:38

score 106 · Answer 10 · 2018-03-25 22:11:52

106

Views

Creating a generating function of recurrence sequence

Published on 25 Mar 2018 - 22:11

score 253 · Answer 11 · 2018-03-25 23:16:09

253

Views

Generating function of a sequence with a sum

Published on 25 Mar 2018 - 23:16

score 105 · Answer 12 · 2018-03-28 14:37:55

105

Views

How do I show that $h_n=\begin{cases}n!2^{\frac{n}{2}-1} , \text {if $n$ is even} \\ 0, \text{if $n$ is odd} \end{cases}$

Published on 28 Mar 2018 - 14:37

score 197 · Answer 13 · 2018-03-30 05:52:08

197

Views

A doubt about 'convergence in distribution implies convergence in probability generating function'

Published on 30 Mar 2018 - 5:52

score 1k · Answer 14 · 2026-03-25 04:35:09

1k

Views

exponential generating function - Fibonacci recurrence relation

Published on 25 Mar 2026 - 4:35

score 116 · Answer 15 · 2018-03-31 15:38:48

116

Views

Property of generating function involving $I_n(k)$, number of permutations in a set of size $n$ that have $k$ inversions

Published on 31 Mar 2018 - 15:38

List Question

Solve the recursion $a_{n+1} = a_n\left(1+\frac{1}{n}\right) +1; a_1=1$

What is the value of the second derivative of a probability generating function?

Set and Inequality, something like generating function.

Calculating the coefficient of $x^k$

Expectation and variance of 4th generation

How does $(a_0+a_1x+a_2x^2+a_3x^3+\cdots)^k$ become $\sum_{n\geq 0}\big(\sum_{i_1+\cdots+i_k=n\\ i_{ij}\geq 0} a_{i_1}a_{i_2}\cdots a_{i_k}\big)x^n$?

Create the generating function for this distribution problem.

How To Apply and Understand the Generating Function for Number Partitioning

N-th term of generating function of almost fibonacci sequence

Creating a generating function of recurrence sequence

Generating function of a sequence with a sum

How do I show that $h_n=\begin{cases}n!2^{\frac{n}{2}-1} , \text {if $n$ is even} \\ 0, \text{if $n$ is odd} \end{cases}$

A doubt about 'convergence in distribution implies convergence in probability generating function'

exponential generating function - Fibonacci recurrence relation

Property of generating function involving $I_n(k)$, number of permutations in a set of size $n$ that have $k$ inversions

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