A202582 Inverse binomial transform of A144691.

1, 0, 1, 0, 19, 0, 515, 0, 74383, 0, 6816465, 0, 1457117673, 0, 241183200687, 0, 188350353304919, 0, 60855583632497865, 0, 39858196864723826583, 0, 17024263169695049621551, 0, 20817292362271689177123509, 0, 13408255577123563666760376685, 0

Offset: 0

Author

Paul D. Hanna, Dec 21 2011

Keywords

• nonn

Comments

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).

Examples

			G.f.: A(x) = 1 + x^2 + 19*x^4 + 515*x^6 + 74383*x^8 + 6816465*x^10 +...
where
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 +...
The g.f. G(x) of A144692 begins:
G(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
where G(x) satisfies: A(x) = G(x*A(x))/(1+x) and G(x) = A(x/(G(x)-x)) + x.
		

Crossrefs

Cf. A144691, A144692, A144690.

Formula

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.