OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..26
FORMULA
E.g.f.: Sum_{k>=0} (exp(k^k*x) - 1)^k.
G.f.: Sum_{k>=0} k! * (k^k*x)^k/Product_{j=1..k} (1 - k^k*j*x).
a(n) ~ n! * n^(n^2). - Vaclav Kotesovec, Feb 04 2022
MAPLE
a:= n-> add(k!*k^(k*n)*Stirling2(n, k), k=0..n):
seq(a(n), n=0..10); # Alois P. Heinz, Feb 01 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[k! * k^(k*n) * StirlingS2[n, k], {k, 1, n}]; Array[a, 9, 0] (* Amiram Eldar, Feb 02 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*k^(k*n)*stirling(n, k, 2));
(PARI) my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (exp(k^k*x)-1)^k)))
(PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, k!*(k^k*x)^k/prod(j=1, k, 1-k^k*j*x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2022
STATUS
approved