OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..51
FORMULA
E.g.f: Sum_{k>=0} x^k / (k! * (1 - k^k * x)).
log(a(n)) ~ n^2*log(n)/4 * (1 - log(2)/log(n) + 1/(4*log(n)^2)). - Vaclav Kotesovec, Nov 27 2022
MATHEMATICA
Table[n!*(1 + Sum[k^(k*(n-k))/k!, {k, 1, n}]), {n, 0, 12}] (* Vaclav Kotesovec, Nov 27 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, k^(k*(n-k))/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^k*x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 22 2022
STATUS
approved