A380778 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x / (1 + x)^2) / (1 + x)^2 ).
1, 3, 21, 238, 3777, 77616, 1966381, 59379888, 2085295617, 83580555520, 3767468068581, 188731359078912, 10405256927541889, 626236791181897728, 40860738460515664125, 2873352871221375440896, 216652727562188159522049, 17437704874236857627246592, 1492289181734461545084103477
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=1, s=1, t=-2, u=2) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);
Formula
E.g.f. A(x) satisfies A(x) = exp( x * A(x) / (1 + x*A(x))^2 ) * (1 + x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n-2*k+2,n-k)/k!.