A343899 a(n) = Sum_{k=0..n} (k!)^k * binomial(n,k).

1, 2, 7, 232, 332669, 24884861086, 139314218808181027, 82606412229102532926819812, 6984964247802365417561163907914436537, 109110688415634181158572146813823590758078301022074, 395940866122426284350759726810156652343313286283891529199276099071

Offset

0,2

Comments

Binomial transform of (n!)^n.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..30

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A048560 A261267 A020459 * A088106 A343928 A294827

Adjacent sequences: A343896 A343897 A343898 * A343900 A343901 A343902

Keyword

nonn

Author

Seiichi Manyama, May 03 2021

Status

approved