A318365 Expansion of e.g.f. exp(x*exp(-x)/(1 - x)).

1, 1, 1, 4, 21, 116, 805, 6504, 59353, 608320, 6901641, 85824080, 1160786341, 16959401304, 266133942061, 4463567862376, 79669223849265, 1507610621184224, 30145968665822737, 635066714078714016, 14057275047440540221, 326159212986987669640, 7915118313077599105461, 200503241124736099689656

Offset

0,4

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A000240(k)*binomial(n-1,k-1)*a(n-k).

a(n) ~ exp(exp(-1)/2 - 1/4 + 2*exp(-1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - Vaclav Kotesovec, Aug 25 2018

Maple

seq(n!*coeff(series(exp(x*exp(-x)/(1-x)), x=0, 24), x, n), n=0..23); # Paolo P. Lava, Jan 09 2019

Mathematica

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

Prog

(PARI) x = 'x + O('x^25); Vec(serlaplace(exp(x*exp(-x)/(1 - x)))) \\ Michel Marcus, Aug 25 2018

Crossrefs

Cf. A000166, A000240, A000262, A003725, A318364.

Sequence in context: A180908 A212419 A020048 * A093426 A182435 A046090

Adjacent sequences: A318362 A318363 A318364 * A318366 A318367 A318368

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 24 2018

Status

approved