A358688 a(n) = n! * Sum_{k=0..n} k^(k * (n-k)) / (n-k)!.

1, 2, 5, 34, 869, 75866, 28213327, 39049033346, 256215628707257, 7710689746589777938, 1063776147486867074877851, 870059224717752809087935599002, 3104894940194751778363241199111802885, 77521065749331962430758061530260243383954602

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..51

Formula

E.g.f.: Sum_{k>=0} x^k * exp(k^k * x).

G.f.: Sum_{k>=0} k! * x^k / (1 - k^k * x)^(k+1).

Mathematica

Table[1 + n!*Sum[k^(k*(n-k))/(n-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))/(n-k)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k*exp(x)^k^k)))
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1-k^k*x)^(k+1)))

Crossrefs

Cf. A006153, A193421, A358687.

Cf. A349893, A356674.

Sequence in context: A283111 A206830 A277436 * A002665 A192222 A326946

Adjacent sequences: A358685 A358686 A358687 * A358689 A358690 A358691

Keyword

nonn

Author

Seiichi Manyama, Nov 26 2022

Status

approved