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G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x)) )^3.
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%I #10 Aug 24 2023 07:48:19

%S 1,3,24,241,2739,33513,430777,5736027,78428376,1094690208,15533884197,

%T 223429310925,3250094373788,47730565667898,706726767511254,

%U 10538728632234471,158132963455869912,2385819265581499593,36171764848848749205,550803320282727312804

%N G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x)) )^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(s*k,n-k)/(n+k+1).

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

%Y Cf. A001002, A365153.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 23 2023