A293848 E.g.f.: exp(Sum_{n>=1} n^n*x^n).

1, 1, 9, 187, 7033, 421341, 37025881, 4500154639, 723834652017, 148905928574713, 38133707320119241, 11894979981772431171, 4439223538343665367209, 1952818695816854110909717, 999887879061130705615605273, 589500991222520435444933020951

Offset: 0

Author

Seiichi Manyama, Oct 17 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..232

Crossrefs

Cf. A000312, A293847, A293849.

Programs

Mathematica

nmax = 20; CoefficientList[Series[E^Sum[k^k*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)

PARI

{a(n) = n!*polcoeff(exp(sum(k=1, n, k^k*x^k)+x*O(x^n)), n)}

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k^(k+1)*a(n-k)/(n-k)! for n > 0.

a(n) ~ n! * n^n. - Vaclav Kotesovec, Oct 18 2017