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G.f. satisfies A(x) = 1 + x*A(x)^2 * (1 + x*A(x)^2)^2.
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%I #9 Nov 12 2023 04:35:59

%S 1,1,4,18,94,527,3108,18993,119214,763997,4978304,32883853,219690066,

%T 1481858835,10078051830,69030877581,475795428158,3297527987794,

%U 22965847261928,160649189379029,1128201207643744,7951399289858530,56222323349767666

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

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

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

%Y Cf. A002293, A073155, A214372, A367283.

%Y Cf. A000108, A367258.

%Y Cf. A367237.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 12 2023