A322535 Number of arrays of 8 integers in -n..n with sum zero.

1, 1107, 38165, 398567, 2306025, 9377467, 30162301, 82073295, 197018321, 429042211, 864287973, 1633586615, 2927984825, 5017519755, 8273550157, 13194953119, 20438495649, 30853690355, 45522444469, 65803811463, 93384154505, 130333031003, 179165107485, 242908414063

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 (8, -28, 56, -70, 56, -28, 8, -1).

Crossrefs

Row 8 of A201552.

Programs

Mathematica

a[n_] := Coefficient[Expand[Sum[x^k, {k, 0, 2n}]^8, x], x, 8n]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

PARI

{a(n) = polcoeff((sum(k=0, 2*n, x^k))^8, 8*n, x)}

Formula

a(n) = [x^(8*n)] (Sum_{k=0..2*n} x^k)^8.

a(n) = (2*n+1)*(9664*n^6+28992*n^5+37360*n^4+26400*n^3+10936*n^2+2568*n+315)/315.