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, 32795665902734099555845

Offset: 0

Author

Seiichi Manyama, Dec 14 2018

Keywords

• nonn

Links

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

Crossrefs

Column 9 of A201552.

Programs

Maple

seq(add((-1)^k*binomial(n, k)*binomial(10*n-19*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, 18}]^n], x^(9n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

PARI

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

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