A155862 A 'Morgan Voyce' transform of A007854.

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

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).

a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*A007854(k) = Sum_{k=0..n} A085478(n,k) * A007854(k).

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

Cf. A001850, A007854, A085478.

Sequence in context: A370695 A086682 A261399 * A088536 A066380 A180899

Adjacent sequences: A155859 A155860 A155861 * A155863 A155864 A155865

Keyword

easy,nonn

Author

Paul Barry, Jan 29 2009

Status

approved