OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n,k) * binomial(k,2).
a(n) = Sum_{k=0..n} binomial(n,k) * Stirling2(k,2) * A000587(n-k).
MATHEMATICA
nmax = 26; CoefficientList[Series[Exp[1 - Exp[x]] (Exp[x] - 1)^2/2, {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k StirlingS2[n, k] Binomial[k, 2], {k, 0, n}], {n, 0, 26}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 07 2024
STATUS
approved