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

0,5

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).

Links

Table of n, a(n) for n=0..27.

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.

Example

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.

Sequence in context: A055967 A366110 A317447 * A292605 A338873 A040365

Adjacent sequences: A202579 A202580 A202581 * A202583 A202584 A202585

Keyword

nonn

Author

Paul D. Hanna, Dec 21 2011

Status

approved