A343898 a(n) = Sum_{k=0..n} (k!)^3 * binomial(n,k).

1, 2, 11, 244, 14741, 1799366, 383827807, 130673579576, 66583061972009, 48379301165408266, 48265538214413425331, 64129741094923528310012, 110669722298686436099306941, 242891356723607474283206170574, 665950191893557715599111566813191, 2246102991406652396042587363523672896

Offset: 0

Author

Seiichi Manyama, May 03 2021

Keywords

• nonn

Comments

Binomial transform of (n!)^3.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..181

Crossrefs

Cf. A000522, A046662, A343899, A343900.

Programs

Mathematica

a[n_] := Sum[(k!)^3 * Binomial[n, k], {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, May 05 2021 *)

PARI

a(n) = sum(k=0, n, k!^3*binomial(n, k));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!^3*x^k/(1-x)^(k+1)))

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, k!^2*x^k)))

Formula

G.f.: Sum_{k>=0} (k!)^3 * x^k/(1 - x)^(k+1).

E.g.f.: exp(x) * Sum_{k>=0} (k!)^2 * x^k.

a(n) ~ (n!)^3. - Vaclav Kotesovec, May 03 2021