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

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

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 *)

Crossrefs

Cf. A059297.

Sequence in context: A287389 A233175 A347920 * A070901 A079657 A136309

Adjacent sequences: A367270 A367271 A367272 * A367274 A367275 A367276

Keyword

sign

Author

Peter Luschny, Nov 11 2023

Status

approved