A372202 E.g.f. A(x) satisfies A(x) = exp( 2 * x * (1 + x * A(x)^(1/2))^2 ).
1, 2, 12, 92, 1024, 14192, 241624, 4855832, 112887520, 2981919392, 88274138344, 2896196131688, 104341759873168, 4096112838853232, 174063938788299928, 7961816811743462648, 390072804802178286016, 20381525361707872355648, 1131437006755346662551496
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=2, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);
Formula
E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A363744.
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!.