This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322539 #18 Oct 19 2024 13:39:32 %S A322539 1,1,19,271,4579,78151,1363573,24072133,429042211,7702189345, %T A322539 139071924069,2522948398895,45949039890469,839611990929219, %U A322539 15385356833972711,282616668487409521,5202536118941844771,95950964483217949751,1772592132899627652691,32795665902734099555845 %N A322539 Number of arrays of n integers in -9..9 with sum zero. %H A322539 Seiichi Manyama, <a href="/A322539/b322539.txt">Table of n, a(n) for n = 0..300</a> %F A322539 a(n) = [x^(9*n)] (Sum_{k=0..18} x^k)^n. %F A322539 a(n) ~ 19^n / (2*sqrt(15*Pi*n)). - _Vaclav Kotesovec_, Dec 15 2018 %p A322539 seq(add((-1)^k*binomial(n, k)*binomial(10*n-19*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # _Peter Bala_, Oct 19 2024 %t A322539 a[n_] := If[n==0, 1, Coefficient[Expand[Sum[x^k, {k, 0, 18}]^n], x^(9n)]]; Array[a, 25, 0] (* _Amiram Eldar_, Dec 14 2018 *) %o A322539 (PARI) {a(n) = polcoeff((sum(k=0, 18, x^k))^n, 9*n, x)} %Y A322539 Column 9 of A201552. %K A322539 nonn %O A322539 0,3 %A A322539 _Seiichi Manyama_, Dec 14 2018