OFFSET
0,2
COMMENTS
Hankel transform is 3^n*2^binomial(n+1, 2).
Image of A007854 by Riordan array (1/(1-x), x/(1-x)^2).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: 2/(3*sqrt(1-6*x+x^2) + x - 1).
G.f.: 1/(1 -x -3*x/(1 -x -x/(1 -x -x/(1 -x -x/(1 -x -x/(1- ... (continued fraction).
2*n*a(n) +(18-25*n)*a(n-1) + 41*(2*n-3)*a(n-2) +(57-25*n)*a(n-3) +2*(n-3)*a(n-4) =0. - R. J. Mathar, Nov 14 2011
a(n) ~ (1+3/sqrt(17)) * (13+3*sqrt(17))^n / 2^(2*n+2). - Vaclav Kotesovec, Feb 01 2014
MATHEMATICA
CoefficientList[Series[2/(3*Sqrt[1-6*x+x^2]+x-1), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(3*Sqrt(1-6*x+x^2) +x -1) )); // G. C. Greubel, Jun 04 2021
(Sage)
def A155862_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 2/(3*sqrt(1-6*x+x^2) +x-1) ).list()
A155862_list(30) # G. C. Greubel, Jun 04 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 29 2009
STATUS
approved