New posts in Generating Functions

Stirling numbers of the second kind: How to obtain a recurrence relation from a generating function?

Partitions of $n$ with exactly 3 parts

Splitting $r^k (r+n)!$ as a sum of factorials

Number of sequences of length $m$ such that $1$ is never followed immediately by $0$

Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?

A sequence of coefficients of $x+(x+(x+(x+(x+(x+\dots)^6)^5)^4)^3)^2$

How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

How can I rewrite recursive function as single formula?

How many ways to choose $a<b<c<d<e$ from the set $\{1,2,3,\dotsc,100\}$ such that $100<a+b+c+d+e<145$?

Words built from $\{0,1,2\}$ with restrictions which are not so easy to accomodate.