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A202582 Inverse binomial transform of A144691. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A221749 A055967 A317447 * A292605 A338873 A040365

Adjacent sequences:  A202579 A202580 A202581 * A202583 A202584 A202585

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 21 2011

STATUS

approved

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Last modified July 26 14:45 EDT 2021. Contains 346294 sequences. (Running on oeis4.)