A277506 E.g.f.: 1/((1+LambertW(-x))*(1-x)).
1, 2, 8, 51, 460, 5425, 79206, 1377985, 27801096, 637630353, 16376303530, 465451009441, 14501512561548, 491394769892377, 17991533604051294, 707766894441628785, 29771014384775612176, 1333347506427522171169, 63346663190991936656466, 3182006256289160385596833
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..385
Crossrefs
Cf. A277507.
Programs
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Maple
a:= proc(n) a(n):= n*a(n-1) + n^n end: a(0):= 1: seq(a(n), n=0..23); # Alois P. Heinz, May 12 2021
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Mathematica
CoefficientList[Series[1/(1+LambertW[-x])/(1-x), {x, 0, 20}], x] * Range[0, 20]! Flatten[{1, Table[n! + Sum[Binomial[n, k]*k^k*(n-k)!, {k, 1, n}], {n, 1, 20}]}] -
PARI
x='x+O('x^50); Vec(serlaplace(1/((1 + lambertw(-x))*(1-x)))) \\ G. C. Greubel, Nov 12 2017
Formula
For n > 0, a(n) = n! + Sum_{k=1..n} binomial(n,k) * k^k * (n-k)!.
a(n) ~ n^n / (1-exp(-1)).
a(n) = n*a(n-1) + n^n, a(0) = 1. - Alois P. Heinz, May 12 2021