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%I #12 Dec 06 2024 11:10:31
%S 1,3,6,22,93,417,1993,9864,50217,261239,1382448,7418877,40278175,
%T 220830513,1220930337,6799458685,38107621704,214771481163,
%U 1216457185122,6920603372448,39529745832681,226605757331904,1303291125124071,7518151040142000,43488151271999326
%N G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)^(4/3)) )^3.
%F G.f.: A(x) = (1 + x*B(x))^3 where B(x) is the g.f. of A364743.
%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=3, s=1, t=0, u=4) = 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. A364743, A371612, A378732.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 05 2024