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 A369403 #14 Feb 16 2024 09:53:53
%S A369403 1,3,12,58,318,1887,11775,76041,503607,3401326,23337339,162214074,
%T A369403 1139835938,8083530360,57783277608,415904602938,3011669994078,
%U A369403 21924967877547,160374157346266,1178091991206162,8687419007293458,64285383562018856,477208235856114384
%N A369403 Expansion of (1/x) * Series_Reversion( x / (1+x)^3 * (1-x^3)^3 ).
%H A369403 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369403 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(3*n+3,n-3*k).
%F A369403 a(n) = (1/(n+1)) * [x^n] ( (1+x)^3 / (1-x^3)^3 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A369403 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)^3*(1-x^3)^3)/x)
%o A369403 (PARI) a(n, s=3, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
%Y A369403 Cf. A369301, A370218.
%K A369403 nonn
%O A369403 0,2
%A A369403 _Seiichi Manyama_, Jan 22 2024