All Questions

Let $a(n)$ be A079501 (i.e., number of compositions of the integer $n$ with strictly smallest part in the first position). The sequence begins with $$ 1, 1, 2, 2, 4, 5, 8, 12, 19, 28, 45, 70, 110, ...

I am interested in the following sequence: $$ T_n = \sum\limits^{n-1}_{k=0} \begin{pmatrix} n \\ k \end{pmatrix} T_{k}, \ \ \ \ T_0 = C \in \mathbb{N} $$ I would like to express it as a function of n, ...

In a recent calculation I obtain a result involving the following expression depending on two integers $n,m\geq 0$: $$S(n,m):=\frac{(n+m+1)!}{n!m!}\sum_{l=0}^{n+m}\frac{1}{n+m-l+1}\sum_{\substack{j+k=...

Let $a(n)$ be A000085, i.e., the number of self-inverse permutations on $n$ letters, also known as involutions; number of standard Young tableaux with $n$ cells. Here $$a(n) = a(n-1) + (n-1)a(n-2), a(...

The sequence $a_n=\sum_{k=0}^n\binom{n}k^24^k$ is listed on OEIS along with a couple of combinatorial interpretations. What interested me at the moment is the plethora of binomial single-sums for the ...