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 A369266 #17 Feb 15 2024 04:18:41
%S A369266 1,1,2,7,24,84,313,1209,4769,19166,78253,323570,1352122,5701467,
%T A369266 24229122,103663575,446163435,1930390329,8391341664,36630504952,
%U A369266 160509484616,705750073063,3112865367660,13769327908980,61066953746400,271488240652950,1209671359828154
%N A369266 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^3)^2 ).
%H A369266 P. Bala, <a href="/A251592/a251592.pdf">Fractional iteration of a series inversion operator</a>
%H A369266 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369266 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(2*n-3*k,n-3*k).
%F A369266 a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^3)^2 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369266 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+x^3)^2)/x)
%o A369266 (PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
%Y A369266 Cf. A071969, A369268.
%Y A369266 Cf. A369267, A370248.
%K A369266 nonn
%O A369266 0,3
%A A369266 _Seiichi Manyama_, Jan 18 2024