A331797 E.g.f.: (exp(x) - 1) * exp(exp(x) - 1) / (2 - exp(x)).
0, 1, 5, 28, 183, 1401, 12466, 127443, 1478581, 19239274, 277797577, 4409962349, 76355817104, 1432117088325, 28925947345561, 625973017346996, 14449435509751843, 354384392492622789, 9202836581079864186, 252260861877820739167, 7278710020682729662089
Offset: 0
Keywords
Programs
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Mathematica
nmax = 20; CoefficientList[Series[(Exp[x] - 1) Exp[Exp[x] - 1]/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]! A007526[n_] := n! Sum[1/k!, {k, 0, n - 1}]; a[n_] := Sum[StirlingS2[n, k] A007526[k], {k, 0, n}]; Table[a[n], {n, 0, 20}] Table[(1/2) Sum[Binomial[n, k] HurwitzLerchPhi[1/2, -k, 0] BellB[n - k], {k, 1, n}], {n, 0, 20}]
Formula
a(n) = Sum_{k=0..n} Stirling2(n,k) * A007526(k).
a(n) ~ n! * exp(1) / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Jan 26 2020
Comments