A322536 Number of arrays of 9 integers in -n..n with sum zero.

1, 3139, 180325, 2636263, 19610233, 97464799, 370487485, 1163205475, 3164588407, 7702189345, 17148949027, 35500063501, 69161990275, 128000343121, 226698100687, 386480229085, 637265493637, 1020310909975, 1591418959705, 2424782370859, 3617545938373, 5295169534843

Offset: 0

Author

Seiichi Manyama, Dec 14 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

Row 9 of A201552.

Programs

Mathematica

a[n_] := Coefficient[Expand[Sum[x^k, {k, 0, 2n}]^9, x], x, 9n]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

PARI

{a(n) = polcoeff((sum(k=0, 2*n, x^k))^9, 9*n, x)}

Formula

a(n) = [x^(9*n)] (Sum_{k=0..2*n} x^k)^9.