A025577 Expansion of (x/(1-x))*sqrt((1+x)/(1-3*x)).

1, 3, 7, 17, 43, 113, 305, 839, 2339, 6585, 18677, 53283, 152725, 439455, 1268623, 3672457, 10656691, 30988249, 90275989, 263425651, 769801873, 2252531971, 6599018227, 19353381877, 56814946381, 166940119063, 490930181515, 1444813563869

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Sum{T(k, k-1), k = 1, 2, ..., n}, where T is the array defined in A025564.

Partial sums of A025565.

Programs

Mathematica

CoefficientList[Series[(x/(1-x))Sqrt[(1+x)/(1-3x)],{x,0,30}],x] (* Harvey P. Dale, Oct 17 2016 *)

PARI

x='x+O('x^50); Vec((x/(1-x))*sqrt((1+x)/(1-3*x))) \\ G. C. Greubel, Feb 15 2017

Formula

a(n) ~ 3^(n-1/2)/(sqrt(Pi*n)). - Vaclav Kotesovec, Jun 29 2013

Conjecture: (-n+1)*a(n) +3*(n-1)*a(n-1) +(n-7)*a(n-2) +3*(-n+3)*a(n-3)=0. - R. J. Mathar, Jul 02 2018

Extensions

G.f. from Vladeta Jovovic, Jan 17 2004