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 A365843 #18 Nov 28 2024 04:00:57
%S A365843 1,6,54,578,6810,85278,1113854,15004746,206955378,2908113974,
%T A365843 41484917958,599202514578,8745727050762,128790559374030,
%U A365843 1911191826600462,28551332345784730,429040549473424866,6480799118506040934,98349636147075506006,1498732955394826784226
%N A365843 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1+x)^3 ).
%F A365843 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(3*(n+1),n-k).
%F A365843 G.f.: B^3, where B is the g.f. of A144097.
%F A365843 a(n) ~ sqrt(8060 + 2651*sqrt(10)) * (223 + 70*sqrt(10))^n / (2 * sqrt(5*Pi) * n^(3/2) * 3^(3*n + 5/2)). - _Vaclav Kotesovec_, Nov 28 2024
%o A365843 (PARI) a(n) = sum(k=0, n, binomial(3*n+k+2, k)*binomial(3*(n+1), n-k))/(n+1);
%Y A365843 Column k=3 of A378238.
%Y A365843 Cf. A007297, A365842, A365844, A365845.
%Y A365843 Cf. A032349, A365622, A365847.
%Y A365843 Cf. A144097.
%K A365843 nonn
%O A365843 0,2
%A A365843 _Seiichi Manyama_, Sep 20 2023