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G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^2 )^3.
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%I #15 Aug 24 2023 07:49:46

%S 1,3,27,301,3780,51030,723170,10611594,159845946,2457515235,

%T 38406398016,608330707740,9744053489754,157564967282709,

%U 2568706865998272,42173100349112852,696692754641035014,11572241797209975966,193153224033985241217

%N G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^2 )^3.

%F If g.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n+k+1).

%o (PARI) a(n, s=2, t=3) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n+k+1));

%Y Cf. A011270, A365148.

%Y Cf. A365121, A365134.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 23 2023