A380780 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)) / (1 + x)^2 ).
1, 3, 27, 436, 10353, 326856, 12920731, 614694816, 34223383809, 2184028353280, 157223422977531, 12606338448248832, 1114292924502666673, 107657947282494206976, 11287975339133863810875, 1276603658863119005618176, 154909721707963344338403969, 20076669149268201122957819904
Offset: 0
Keywords
Programs
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PARI
a(n, q=1, r=1, s=1, t=1, 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)) ) * (1 + x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+k+2,n-k)/k!.