%I #18 Mar 29 2024 15:21:22
%S 1,2,15,138,1435,16074,189238,2308640,28927579,370084760,4814147248,
%T 63482437724,846678807008,11401357736202,154800183842738,
%U 2116833422071448,29128279396373599,403029526567463278,5603854904038673961,78260199678455985082,1097257906416031628336
%N G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x*A(x))^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(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).
%o (PARI) a(n, r=2, s=2, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A371579.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 28 2024