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

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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.

Mathematica

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

Prog

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

Crossrefs

Row 8 of A201552.

Sequence in context: A295991 A157376 A185501 * A184370 A172638 A278633

Adjacent sequences: A322532 A322533 A322534 * A322536 A322537 A322538

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2018

Status

approved