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Integer coefficients such that $T(n,k)=R(n,k)-R(n,k-1)$

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(...
Notamathematician's user avatar
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In search of multiple expressions for a sequence

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 ...
T. Amdeberhan's user avatar