A379859 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) * (1 - x*exp(x))^2 ).
1, 1, 9, 110, 2121, 53834, 1720105, 66197578, 2984752113, 154358553986, 9009411908001, 585917934419498, 42018536835853369, 3294423846094650658, 280362373171289449209, 25739124908062020925034, 2535728977438902352557921, 266836955238122741966767874, 29872121613650590137264191665
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(x)*(1-x*exp(x))^2)/x)) -
PARI
a(n) = n!*sum(k=0, n, (-n+k-1)^(n-k)*binomial(2*n+k+1, k)/(n-k)!)/(n+1);
Formula
E.g.f. A(x) satisfies A(x) = exp(-x*A(x))/(1 - x * A(x) * exp(x*A(x)))^2.
a(n) = (n!/(n+1)) * Sum_{k=0..n} (-n+k-1)^(n-k) * binomial(2*n+k+1,k)/(n-k)!.