A343929 a(n) = Sum_{k=0..n} (k!)^(n+1) * binomial(n,k).

1, 2, 11, 1348, 7993925, 2986939982086, 100308280020162672007, 416336818263472141683094788104, 281633775231427434285800695714399092181001, 39594086714441777969538839399390619086007952991080833034

Offset: 0

Author

Seiichi Manyama, May 04 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..29

Crossrefs

Cf. A046662, A343898, A343900, A343928.

Programs

Mathematica

a[n_] := Sum[(k!)^(n+1) * Binomial[n, k], {k, 0, n} ]; Array[a, 10, 0] (* Amiram Eldar, May 04 2021 *)

PARI

a(n) = sum(k=0, n, k!^(n+1)*binomial(n, k));

Formula

a(n) = [x^n] Sum_{k>=0} (k!)^(n+1) * x^k/(1 - x)^(k+1).

a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^n * x^k.