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G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^3 )^3.
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%I #13 Aug 24 2023 07:49:57

%S 1,3,30,361,4887,71064,1084338,17127921,277691055,4594624095,

%T 77271742056,1317037554924,22699836814548,394961294853852,

%U 6928051002350154,122384261274499665,2175295243858562031,38875484049230706129,698131263508514451678

%N G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^3 )^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=3, 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. A365150, A365151.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 23 2023