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%I #7 Mar 30 2012 18:37:33
%S 1,0,1,0,19,0,515,0,74383,0,6816465,0,1457117673,0,241183200687,0,
%T 188350353304919,0,60855583632497865,0,39858196864723826583,0,
%U 17024263169695049621551,0,20817292362271689177123509,0,13408255577123563666760376685,0
%N Inverse binomial transform of A144691.
%C A144691 is defined by: A144691(n) = limit of the coefficient of x^(2^m+n) in B(x)^(n+1)/(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).
%F G.f. A(x) satisfies: x/Series_Reversion(x*A(x)) = G(x) - x, so that G(x*A(x)) = (1+x)*A(x) and A(x/(G(x) - x)) = G(x) - x, where G(x) is the g.f. of A144692.
%e G.f.: A(x) = 1 + x^2 + 19*x^4 + 515*x^6 + 74383*x^8 + 6816465*x^10 +...
%e where
%e x/Series_Reversion(x*A(x)) = 1 + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...+ A144692(n)*x^n +...
%e The g.f. G(x) of A144692 begins:
%e G(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
%e where G(x) satisfies: A(x) = G(x*A(x))/(1+x) and G(x) = A(x/(G(x)-x)) + x.
%Y Cf. A144691, A144692, A144690.
%K nonn
%O 0,5
%A _Paul D. Hanna_, Dec 21 2011
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