A343900 a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).

1, 2, 11, 1324, 7967861, 2986023826166, 100306147958903465407, 416336313421816733159702737376, 281633758448076539969292901914477101456489, 39594086612245054028213574779019294652734771094507399786

Offset: 0

Author

Seiichi Manyama, May 03 2021

Keywords

• nonn

Comments

Binomial transform of (n!)^(n+1).

Links

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

Crossrefs

Cf. A000522, A036740, A046662, A091868, A343898, A343899, A343929.

Programs

Mathematica

a[n_] := Sum[(k!)^(k+1) * Binomial[n, k], {k, 0, n}]; Array[a, 10, 0] (* Amiram Eldar, May 05 2021 *)

PARI

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

PARI

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

PARI

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

Formula

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

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