A379860 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) * (1 - x*exp(x))^2 ).
1, 3, 33, 670, 20201, 813626, 41138953, 2507380618, 179034345393, 14663636270146, 1355499957188321, 139617725163885002, 15858083818590019993, 1969242291969058135810, 265431275379747754496409, 38595876183118645455281386, 6022354171062480540156895457, 1003753282859589405272849735810
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)!.