New posts in Generating Functions

extract Catalan numbers from generating function via residues

If $\sum\limits_{n=1}^{\infty}\frac{1}{p(n)}\in\mathbb{Q}$, is $\sum\limits_{n=1}^{\infty}\frac{n}{p(n)}\in\mathbb{Q}$?

Why would you take the logarithmic derivative of a generating function?

Proof of a Combinatorial Abel Identity

Asymptotics of $e^{-n}\sum_{k=0}^{n-1}\frac{n^k}{k!}\cdot\frac1{n-k}$

Binomial summation $\sum\binom nkk^2$

Why do expressions of the form $\sum\limits^\infty_{n=1} \frac{n^k}{3^n}$ sum 'nicely'?

Infinite geometric sum (asking for insight on an easier solution)

A nice but somewhat challenging binomial identity

Understanding summation of infinite series by defining a new function