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 A369507 #8 Jan 25 2024 07:50:16
%S A369507 1,6,51,508,5535,63888,767689,9502254,120324606,1551362160,
%T A369507 20296839585,268785905790,3595951246855,48528885742200,
%U A369507 659856371680971,9031161933443468,124319953470044970,1720113658097639532,23908612149570793386,333680424238179500976
%N A369507 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^3)^2 ).
%H A369507 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369507 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-3*k).
%o A369507 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^3)^2)/x)
%o A369507 (PARI) a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-3*k))/(n+1);
%Y A369507 Cf. A369483, A369504.
%K A369507 nonn
%O A369507 0,2
%A A369507 _Seiichi Manyama_, Jan 25 2024