A343899 - OEIS

%I #23 May 05 2021 01:55:11

%S 1,2,7,232,332669,24884861086,139314218808181027,

%T 82606412229102532926819812,6984964247802365417561163907914436537,

%U 109110688415634181158572146813823590758078301022074,395940866122426284350759726810156652343313286283891529199276099071

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

%C Binomial transform of (n!)^n.

%H Seiichi Manyama, <a href="/A343899/b343899.txt">Table of n, a(n) for n = 0..30</a>

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

%F E.g.f.: exp(x) * Sum_{k>=0} (k!)^(k-1) * x^k.

%t a[n_] := Sum[(k!)^k * Binomial[n, k], {k, 0, n}]; Array[a, 11, 0] (* _Amiram Eldar_, May 05 2021 *)

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

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

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

%Y Cf. A000522, A036740, A046662, A086331, A343898, A343900, A343928.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 03 2021