A356674 a(n) = n! * Sum_{k=0..n} k^(k*(n-k))/k!.

1, 2, 5, 25, 349, 19941, 4440391, 4382699203, 17687865017481, 356274213630958297, 33338407933090938442411, 16214021627369697901867402911, 43817834057167927861655409052462093, 595284492835035398061242850538179192931525

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

Cf. A354436, A356672, A356673.

Cf. A327578, A349893.

Sequence in context: A015486 A378327 A191951 * A370555 A120767 A051771

Adjacent sequences: A356671 A356672 A356673 * A356675 A356676 A356677

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2022

Status

approved