A277454 a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 2^k * k^k.

1, 3, 21, 271, 5065, 122811, 3651997, 128566663, 5227782161, 241072839667, 12430169195941, 708612945554559, 44253858433505497, 3004570398043291819, 220341964157226260525, 17357760973540312138231, 1461813975265547356467745, 131061164660246579394042339

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..351

Crossrefs

Cf. A086331, A277456.

Programs

Mathematica

Table[1+Sum[Binomial[n, k]*2^k*k^k, {k, 1, n}], {n, 0, 20}]
CoefficientList[Series[E^x/(1+LambertW[-2*x]), {x, 0, 20}], x] * Range[0, 20]!

PARI

{a(n) = sum(k=0, n, binomial(n, k)*(2*k)^k)} \\ Seiichi Manyama, Jan 12 2019

Formula

E.g.f.: exp(x)/(1+LambertW(-2*x)).

a(n) ~ exp(exp(-1)/2) * 2^n * n^n.