A277456 a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 3^k * k^k.

1, 4, 43, 847, 23881, 870721, 38894653, 2055873037, 125480383153, 8684069883409, 671922832985941, 57475677232902589, 5385592533714824521, 548596467532888667257, 60358911366712739334541, 7133453715771227363127301, 901261693601873814393568993

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..333

Crossrefs

Cf. A086331, A277454.

Programs

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

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]!

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

Formula

E.g.f.: exp(x)/(1+LambertW(-3*x)).

a(n) ~ exp(exp(-1)/3) * 3^n * n^n.