A341185 a(n) = Sum_{k=0..n} k^n * k! * binomial(n,k)^2.

1, 1, 12, 315, 15088, 1141625, 124989156, 18659050795, 3638892086208, 897534389449809, 272981684150035300, 100316132701760094251, 43802068733570039425776, 22409162143775383385763913, 13274030650412266312507931652

Offset: 0

Author

Seiichi Manyama, Feb 06 2021

Keywords

• nonn

Crossrefs

Cf. A002720, A332408, A336828, A341197.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k^n * k! * Binomial[n, k]^2, {k, 0, n}]; Array[a, 15, 0] (* Amiram Eldar, Feb 06 2021 *)

PARI

a(n) = sum(k=0, n, k^n*k!*binomial(n, k)^2);