A336181 a(n) = Sum_{k=0..n} (-2)^k * binomial(n,k)^3.

1, -1, -11, 47, 241, -2281, -3779, 104831, -110207, -4415281, 16955269, 161498831, -1252782959, -4376471737, 73606867309, 11876256767, -3715460133887, 9838677757343, 160921055160469, -957644184613393, -5553047963695439, 65231925087461879, 102267746634093469

Offset: 0

Author

Seiichi Manyama, Jul 10 2020

Keywords

• sign

Comments

Diagonal of the rational function 1 / (1 + y + z + x*y + y*z - 2*z*x - x*y*z).

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) + 2*x*y*z).

Crossrefs

Column k=2 of A336179.

Cf. A206178.

Programs

Mathematica

a[n_] := Sum[(-2)^k * Binomial[n, k]^3, {k, 0, n}]; Array[a, 23, 0] (* Amiram Eldar, Jul 11 2020 *)

PARI

{a(n) = sum(k=0, n, (-2)^k*binomial(n, k)^3)}