A322537 Number of arrays of 10 integers in -n..n with sum zero.

1, 8953, 856945, 17538157, 167729959, 1018872811, 4577127763, 16581420835, 51125645317, 139071924069, 342237634221, 775938666273, 1643151128475, 3284313415527, 6247630238079, 11385659856231, 19984965376233, 33936690554865, 55957080110537, 89868204063989, 140950465124591

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 (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Crossrefs

Row 10 of A201552.

Programs

Mathematica

a[n_] := Coefficient[Expand[Sum[x^k, {k, 0, 2n}]^10, x], x, 10n]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

PARI

{a(n) = polcoeff((sum(k=0, 2*n, x^k))^10, 10*n, x)}

Formula

a(n) = [x^(10*n)] (Sum_{k=0..2*n} x^k)^10.