A322539 Number of arrays of n integers in -9..9 with sum zero.

1, 1, 19, 271, 4579, 78151, 1363573, 24072133, 429042211, 7702189345, 139071924069, 2522948398895, 45949039890469, 839611990929219, 15385356833972711, 282616668487409521, 5202536118941844771, 95950964483217949751, 1772592132899627652691

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..300

Formula

a(n) = [x^(9*n)] (Sum_{k=0..18} x^k)^n.

a(n) ~ 19^n / (2*sqrt(15*Pi*n)). - Vaclav Kotesovec, Dec 15 2018

Mathematica

a[n_] := If[n==0, 1, Coefficient[Expand[Sum[x^k, {k, 0, 18}]^n], x^(9n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

Prog

(PARI) {a(n) = polcoeff((sum(k=0, 18, x^k))^n, 9*n, x)}

Crossrefs

Column 9 of A201552.

Sequence in context: A016189 A125476 A016248 * A199819 A016187 A016184

Adjacent sequences: A322536 A322537 A322538 * A322540 A322541 A322542

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2018

Status

approved