A381021 Expansion of e.g.f. log(1-x)^2 * exp(x) / 2.
0, 0, 1, 6, 29, 145, 814, 5243, 38618, 321690, 2995011, 30840304, 348114711, 4274888891, 56744495872, 809667333733, 12358833406580, 200955441549140, 3467781770502885, 63298198354605210, 1218507112218768721, 24671782054230662277, 524152965820457130290
Offset: 0
Keywords
Programs
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Mathematica
nmax=22; CoefficientList[Series[Log[1-x]^2*Exp[x]/2,{x,0,nmax}],x]Range[0,nmax]! (* Stefano Spezia, Feb 12 2025 *) -
PARI
a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(k, 2, 1)));
Formula
a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k,2)|.