New posts in Generating Functions

Let $b_{n}$ denote the number of compositions of $n$ into $k$ parts, where each part is one or two. Find the generating series for $b_{n}$

Question about product of generating functions in a proof that for positive integer $n$, $\sum_{k=0}^n(-1)^k\binom nk\binom{2n-k}n=1$.

$x_{n+13}=x_{n+4}+2x_{n}$, $x_{143}=...$

Closed form of recurrence relation $a_k=(n+k)a_{k-1}-ka_{k-2}$

Somewhat challenging binomial identity

Combinatorial proof of identity involving central binomial coefficients

Is the closed form for $\sum_{k=1}^\infty\frac{\overline{H}_k}{k^m}$ known in the literature?

Prove that $\sum_{k=0}^{\lfloor (n-1)/2 \rfloor} (-1)^k {n+1 \choose k} {2n-2k-1 \choose n} =\frac{ n(n+1)}2 $

Given a natural number $n$ and define $B_n$ as the set of all sequence $b_1, b_2, \dots, b_n$ of length $n$...

Computing the exponential generating function of the Bell numbers.