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 A369269 #16 Feb 15 2024 04:22:06
%S A369269 1,2,7,33,173,962,5586,33498,205846,1289386,8202247,52845855,
%T A369269 344129832,2261377872,14976646685,99863119809,669860309538,
%U A369269 4517037850220,30603008068997,208211448723097,1421986458302466,9745007758311114,66993247112160800
%N A369269 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^3)^3 ).
%H A369269 P. Bala, <a href="/A251592/a251592.pdf">Fractional iteration of a series inversion operator</a>
%H A369269 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369269 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(3*n-3*k+1,n-3*k).
%F A369269 a(n) = (1/(n+1)) * [x^n] ( 1/(1-x)^2 * (1+x^3)^3 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369269 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^3)^3)/x)
%o A369269 (PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
%Y A369269 Cf. A369268, A369270.
%Y A369269 Cf. A369265, A369267.
%K A369269 nonn
%O A369269 0,2
%A A369269 _Seiichi Manyama_, Jan 18 2024