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%I #10 Jan 17 2024 09:35:48
%S 1,1,4,15,65,298,1429,7073,35869,185403,973198,5173644,27797914,
%T 150715321,823541564,4530609391,25073291597,139492998775,779706274423,
%U 4376600956063,24659875131049,139424357994344,790763858547445,4497788153203946,25650342635871106
%N Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^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/2)} binomial(2*n+2,k) * binomial(2*n-k,n-2*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^2)^2)/x)
%o (PARI) a(n, s=2, t=2, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y Cf. A366049, A369230.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jan 17 2024