A321989 Expansion of e.g.f. exp(exp(-x)/(1 - x) - 1).

1, 0, 1, 2, 12, 64, 455, 3618, 33131, 338728, 3838572, 47678520, 644172045, 9402091620, 147405489205, 2470129035710, 44053120590540, 833000495161600, 16644648834503555, 350406040769989974, 7751328201878523295, 179738821179613739780, 4359334293132050359932, 110368937036048741434824

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A000166(k)*binomial(n-1,k-1)*a(n-k).

a(n) ~ exp(3*exp(-1)/2 - 5/4 + 2*exp(-1/2)*sqrt(n) - n) * n^(n-1/4) / sqrt(2). - Vaclav Kotesovec, Dec 19 2018

Maple

seq(coeff(series(factorial(n)*exp(exp(-x)/(1-x)-1), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Dec 19 2018

Mathematica

nmax = 23; CoefficientList[Series[Exp[Exp[-x]/(1 - x) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Subfactorial[k] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

Crossrefs

Cf. A000166, A000262, A318365, A321974.

Sequence in context: A190155 A025599 A162973 * A226226 A126737 A345697

Adjacent sequences: A321986 A321987 A321988 * A321990 A321991 A321992

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 19 2018

Status

approved