A351117 a(n) = Sum_{k=0..n} k! * k^(k*n) * Stirling2(n,k).

1, 1, 33, 118483, 103098350565, 35763050750177408011, 7426387531294259002278007386693, 1294894837982331421844458945612619053737859003, 253092742000650212461957357208907985560332648454746968725711765

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

Cf. A000670, A122399, A229260, A242229.

Cf. A249584.

Sequence in context: A060767 A220350 A300614 * A351138 A171705 A228426

Adjacent sequences: A351114 A351115 A351116 * A351118 A351119 A351120

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2022

Status

approved