A322540 Number of arrays of n integers in -10..10 with sum zero.

1, 1, 21, 331, 6181, 116601, 2248575, 43874139, 864287973, 17148949027, 342237634221, 6862175029689, 138132246844879, 2789732439723061, 56501091296763855, 1147129435985083731, 23339695295337149925, 475767618472211229549, 9714486212587875804351

Offset: 0

Author

Seiichi Manyama, Dec 14 2018

Keywords

• nonn

Links

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

Crossrefs

Column 10 of A201552.

Programs

Maple

seq(add((-1)^k*binomial(n, k)*binomial(11*n-21*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, 20}]^n], x^(10n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

PARI

{a(n) = polcoeff((sum(k=0, 20, x^k))^n, 10*n, x)}

Formula

a(n) = [x^(10*n)] (Sum_{k=0..20} x^k)^n.

a(n) ~ sqrt(3) * 21^n / (2*sqrt(55*Pi*n)). - Vaclav Kotesovec, Dec 15 2018