A322538 Number of arrays of n integers in -8..8 with sum zero.

1, 1, 17, 217, 3281, 50101, 782153, 12354469, 197018321, 3164588407, 51125645317, 829858058019, 13522838817929, 221088393889403, 3624855419439957, 59576725303913167, 981272544393935569, 16192709833199300337, 267654541150392845543, 4430755975190532983531

Offset: 0

Author

Seiichi Manyama, Dec 14 2018

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..350

Crossrefs

Column 8 of A201552.

Programs

Maple

seq(add((-1)^k*binomial(n, k)*binomial(9*n-17*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # Peter Bala, Oct 19 2024

Mathematica

a[n_] := If[n==0, 1, Coefficient[Expand[Sum[x^k, {k, 0, 16}]^n], x^(8n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

PARI

{a(n) = polcoeff((sum(k=0, 16, x^k))^n, 8*n, x)}

Formula

a(n) = [x^(8*n)] (Sum_{k=0..16} x^k)^n.

a(n) ~ 17^n / (4*sqrt(3*Pi*n)). - Vaclav Kotesovec, Dec 15 2018