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 A369262 #17 Feb 15 2024 04:15:34
%S A369262 1,1,5,17,80,363,1792,8969,46319,242994,1296046,6996163,38175142,
%T A369262 210162728,1166020560,6512854409,36593709385,206686641555,
%U A369262 1172856064443,6683348391034,38228129813288,219411037878578,1263245957786120,7293833100110787,42224142505632305
%N A369262 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^2)^3 ).
%H A369262 P. Bala, <a href="/A251592/a251592.pdf">Fractional iteration of a series inversion operator</a>
%H A369262 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369262 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(2*n-2*k,n-2*k).
%F A369262 a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^2)^3 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369262 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+x^2)^3)/x)
%o A369262 (PARI) a(n, s=2, t=3, 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 A369262 Cf. A052709, A369226.
%Y A369262 Cf. A369263, A369264.
%K A369262 nonn
%O A369262 0,3
%A A369262 _Seiichi Manyama_, Jan 18 2024