A358688 - OEIS

%I #16 Nov 27 2022 06:44:34

%S 1,2,5,34,869,75866,28213327,39049033346,256215628707257,

%T 7710689746589777938,1063776147486867074877851,

%U 870059224717752809087935599002,3104894940194751778363241199111802885,77521065749331962430758061530260243383954602

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

%H Seiichi Manyama, <a href="/A358688/b358688.txt">Table of n, a(n) for n = 0..51</a>

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

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

%t Table[1 + n!*Sum[k^(k*(n-k))/(n-k)!, {k, 1, n}], {n, 0, 12}] (* _Vaclav Kotesovec_, Nov 27 2022 *)

%o (PARI) a(n) = n!*sum(k=0, n, k^(k*(n-k))/(n-k)!);

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k*exp(x)^k^k)))

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1-k^k*x)^(k+1)))

%Y Cf. A006153, A193421, A358687.

%Y Cf. A349893, A356674.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 26 2022