|
|
A155862
|
|
A 'Morgan Voyce' transform of A007854.
|
|
1
|
|
|
1, 4, 22, 130, 790, 4870, 30274, 189202, 1186702, 7461982, 47007034, 296527162, 1872479350, 11833642006, 74833075570, 473463268642, 2996771766046, 18974162475598, 120167557286314, 761214481604554, 4822871486667526, 30561172252753030, 193682023673424226, 1227594333811376050, 7781431761074125486
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 2/(3*sqrt(1-6*x+x^2) +x-1) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|