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%I #9 Apr 08 2025 08:47:13
%S 1,2,11,60,365,2350,15767,109048,771993,5567066,40751267,302018484,
%T 2261763205,17088919814,130108591407,997225521136,7688232599089,
%U 59581977618098,463890112373563,3626778446099756,28461425971969693,224114796803735774,1770236735807921863
%N G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^2.
%F G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^2 * A(x)^(3/2) )^2.
%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).
%F G.f.: B(x)^2, where B(x) is the g.f. of A366221.
%o (PARI) a(n, r=2, s=2, t=3, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A073155, A382886.
%Y Cf. A366221.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 08 2025