A380781 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)^2) / (1 + x)^2 ).
1, 3, 29, 514, 13473, 470616, 20607781, 1086800352, 67105960641, 4750972007680, 379512594172941, 33771911612182272, 3313441417839023521, 355371388642280715264, 41365962922892138767125, 5193995331631149377867776, 699785874809076112607739009, 100701968551637581411176480768
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!.