A341197 a(n) = Sum_{k=0..n} k^n * (n-k)! * binomial(n,k)^2.

1, 1, 8, 117, 2800, 97125, 4551876, 274975897, 20690260928, 1889451727497, 205192914235300, 26068434774065541, 3822244304373085680, 639508508456359098349, 120922358829574588363364, 25626415609908102483018225

Offset: 0

Author

Seiichi Manyama, Feb 06 2021

Keywords

• nonn

Crossrefs

Main diagonal of A341200.

Cf. A277373, A341185.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k^n * (n-k)! * Binomial[n, k]^2, {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2021 *)

PARI

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