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

Offset

0,3

Links

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

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

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 *)

Prog

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

Crossrefs

Column 10 of A201552.

Sequence in context: A011810 A091947 A016195 * A016191 A297336 A095905

Adjacent sequences: A322537 A322538 A322539 * A322541 A322542 A322543

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2018

Status

approved