OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..333
FORMULA
E.g.f.: exp(x)/(1+LambertW(-3*x)).
a(n) ~ exp(exp(-1)/3) * 3^n * n^n.
MAPLE
f:= n -> 1 + add(binomial(n, k)*3^k*k^k, k=1..n):
map(f, [$0..20]); # Robert Israel, Oct 30 2016
MATHEMATICA
Table[1 + Sum[Binomial[n, k]*3^k*k^k, {k, 1, n}], {n, 0, 20}]
CoefficientList[Series[E^x/(1+LambertW[-3*x]), {x, 0, 20}], x] * Range[0, 20]!
PROG
(PARI) a(n) = 1 + sum(k=1, n, binomial(n, k) * 3^k * k^k); \\ Michel Marcus, Oct 30 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x)/(1+lambertw(-3*x)))) \\ G. C. Greubel, Sep 09 2018
(Magma) [1] cat [1 + (&+[Binomial(n, k)*3^k*k^k: k in [1..n]]): n in [1..20]]; // G. C. Greubel, Sep 09 2018
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Vaclav Kotesovec, Oct 16 2016
STATUS
approved