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A174403 Expansion of (1-2x-2x^2-sqrt(1-4x-4x^2+8x^3+4x^4))/(2x^2). 1
1, 2, 7, 22, 76, 268, 977, 3638, 13804, 53164, 207342, 817212, 3250104, 13026744, 52567461, 213394854, 870845260, 3570590668, 14701822370, 60765209876, 252021314536, 1048538259304, 4375013741962, 18302920281148, 76756814078840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

G.f. A(x) satisfies A(x)=1+2x*A(x)+2x^2*A(x)+x^2*A(x)^2. Hankel transform is A174404.

LINKS

Table of n, a(n) for n=0..24.

FORMULA

G.f.: 1/(1-2x-2x^2-x^2/(1-2x-2x^2-x^2/(1-... (continued fraction).

Let A(x) be the g.f., then B(x)=1+x*A(x) = 1 +1*x +2*x^2 +7*x^3 +22*x^4 +... = 1/(1-z/(1-z/(1-z/(...)))) where z=x/(1-2*x^2) (continued fraction); more generally B(x)=C(x/(1-2*x^2)) where C(x) is the g.f. for the Catalan numbers (A000108). [Joerg Arndt, Mar 18 2011]

Conjecture: (n+2)*a(n) -2*(2*n+1)*a(n-1) +4*(1-n)*a(n-2) +4*(2*n-5)*a(n-3) +4*(n-4)*a(n-4)=0. - R. J. Mathar, Sep 30 2012

a(n) ~ 6^(1/4) * (2 + sqrt(6))^(n+1) / (sqrt(2*Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 15 2018

CROSSREFS

Sequence in context: A007141 A278151 A090831 * A119975 A106188 A176612

Adjacent sequences:  A174400 A174401 A174402 * A174404 A174405 A174406

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 18 2010

STATUS

approved

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)