%I #21 Jan 23 2024 11:14:12
%S 1,2,5,16,62,264,1170,5310,24599,116090,556569,2703098,13268900,
%T 65721840,328050639,1648535856,8333536002,42348587700,216211838178,
%U 1108514508608,5704874555112,29460504457692,152612723209700,792833380805160,4129639139612133
%N Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3)^2) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(2*n+2,n-3*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x^3)^2))/x)
%o (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial(u*(n+1), n-s*k))/(n+1);
%Y Cf. A369442, A369443.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 23 2024