A367273 a(n) = Sum_{k=0..n} binomial(n, k)^2 * (k - n)^k.

1, 1, -3, -8, 81, 26, -3815, 17494, 178241, -2817746, 3552201, 315952418, -3635118575, -11060115936, 782886068497, -7772807719574, -66097429593855, 2841563213504406, -26634464325602135, -375731325639156710, 14734035378180288401, -142992751647059748944

Offset: 0

Author

Peter Luschny, Nov 11 2023

Keywords

• sign

Crossrefs

Cf. A059297.

Programs

Maple

a := n -> add(binomial(n, k)^2 * (k - n)^k, k = 0..n):
seq(a(n), n = 0..22);

Mathematica

A367273[n_]:=If[n==0,1,Sum[Binomial[n,k]^2(k-n)^k,{k,0,n}]];
Array[A367273,30,0] (* Paolo Xausa, Nov 29 2023 *)

Formula

a(n) = Sum_{k=0..n} (-1)^k * binomial(n, k) * A059297(n, n - k).