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

0,3

Links

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

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

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 *)

Prog

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

Crossrefs

Column 8 of A201552.

Sequence in context: A139733 A016185 A125452 * A016238 A016181 A285233

Adjacent sequences: A322535 A322536 A322537 * A322539 A322540 A322541

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2018

Status

approved