Question

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

score 63 · Answer 1 · 2026-04-16 19:14:11

63

Views

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

Published on 16 Apr 2026 - 19:14

score 595 · Answer 2 · 2026-04-13 03:32:00

595

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

Published on 13 Apr 2026 - 3:32

score 46 · Answer 3 · 2026-05-10 15:41:07

46

Views

Set and Inequality, something like generating function.

Published on 10 May 2026 - 15:41

score 168 · Answer 4 · 2026-04-13 01:14:03

168

Views

Calculating the coefficient of $x^k$

Published on 13 Apr 2026 - 1:14

score 82 · Answer 5 · 2026-04-15 00:01:38

82

Views

Expectation and variance of 4th generation

Published on 15 Apr 2026 - 0:01

score 54 · Answer 6 · 2026-04-13 16:26:09

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 73 · Answer 7 · 2026-04-14 00:53:47

73

Views

Create the generating function for this distribution problem.

Published on 14 Apr 2026 - 0:53

score 427 · Answer 8 · 2026-05-10 14:04:20

427

Views

How To Apply and Understand the Generating Function for Number Partitioning

Published on 10 May 2026 - 14:04

score 137 · Answer 9 · 2026-05-10 16:01:06

137

Views

N-th term of generating function of almost fibonacci sequence

Published on 10 May 2026 - 16:01

score 108 · Answer 10 · 2026-04-07 18:04:56

108

Views

Creating a generating function of recurrence sequence

Published on 07 Apr 2026 - 18:04

score 256 · Answer 11 · 2026-04-12 13:39:35

256

Views

Generating function of a sequence with a sum

Published on 12 Apr 2026 - 13:39

score 108 · Answer 12 · 2026-04-16 00:07:29

108

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 16 Apr 2026 - 0:07

score 200 · Answer 13 · 2026-04-10 16:12:05

200

Views

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

Published on 10 Apr 2026 - 16:12

score 1k · Answer 14 · 2026-05-10 14:53:47

1k

Views

exponential generating function - Fibonacci recurrence relation

Published on 10 May 2026 - 14:53

score 119 · Answer 15 · 2026-04-15 20:12:14

119

Views

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

Published on 15 Apr 2026 - 20:12

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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