OFFSET
0,3
COMMENTS
Stirling transform of A007526.
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
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 26 2020
STATUS
approved