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 A369263 #18 Feb 15 2024 04:16:15
%S A369263 1,2,10,54,329,2126,14356,100030,713956,5193064,38354066,286860714,
%T A369263 2168308302,16537766036,127114940840,983657456878,7657060437148,
%U A369263 59917814944376,471062428422152,3718952705982232,29471640802526185,234356062245289566,1869405604537134116
%N A369263 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^2)^3 ).
%H A369263 P. Bala, <a href="/A251592/a251592.pdf">Fractional iteration of a series inversion operator</a>
%H A369263 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369263 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(3*n-2*k+1,n-2*k).
%F A369263 a(n) = (1/(n+1)) * [x^n] ( 1/(1-x)^2 * (1+x^2)^3 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369263 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^2)^3)/x)
%o A369263 (PARI) a(n, s=2, 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 A369263 Cf. A218045, A369208.
%Y A369263 Cf. A369262, A369264.
%Y A369263 Cf. A370245.
%K A369263 nonn
%O A369263 0,2
%A A369263 _Seiichi Manyama_, Jan 18 2024