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E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * (1 + x * A(x)) ).
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%I #11 Apr 21 2024 11:40:53

%S 1,2,12,122,1800,35002,848236,24664362,837602352,32558200370,

%T 1426118691924,69522324440098,3733960438696648,219101400537409002,

%U 13946923555466389884,957297896801470079258,70483467144263313405024,5541471459106022647303522

%N E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * (1 + x * A(x)) ).

%F E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A363355.

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

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

%Y Cf. A363355, A372164, A372179.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 21 2024