OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
FORMULA
a(n) ~ exp(2*exp(-1)) * n^n.
MATHEMATICA
CoefficientList[Series[Exp[2*x]/(1+LambertW[-x]), {x, 0, 20}], x]*Range[0, 20]!
Table[1 + Sum[Binomial[n, m]*(1 + Sum[Binomial[m, k]*k^k, {k, 1, m}]), {m, 1, n}], {n, 0, 20}]
Table[2^n + Sum[Binomial[n, k]*2^(n-k)*k^k, {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)
PROG
(PARI) x='x+O('x^50); Vec(serlaplace(exp(2*x)/(1 + lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 16 2016
STATUS
approved