A322537 - OEIS

%I #15 Oct 01 2024 11:04:13

%S 1,8953,856945,17538157,167729959,1018872811,4577127763,16581420835,

%T 51125645317,139071924069,342237634221,775938666273,1643151128475,

%U 3284313415527,6247630238079,11385659856231,19984965376233,33936690554865,55957080110537,89868204063989,140950465124591

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

%H Seiichi Manyama, <a href="/A322537/b322537.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

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

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

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

%Y Row 10 of A201552.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 14 2018