A108781 Expansion of sqrt((1-x+8*x^2)/(1-x)^3).

1, 1, 5, 9, 5, -7, 5, 73, 69, -295, -571, 1321, 4613, -4167, -32635, -1783, 211141, 200601, -1229243, -2468375, 6117509, 22557305, -21519611, -176980023, -13664955, 1234115673, 1250908869, -7608051031, -16094268667, 39424807225, 153179607429, -139981878647, -1243776268859

Offset: 0

Author

N. J. A. Sloane and Nadia Heninger, Jun 28 2005

Keywords

• sign

Links

• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.
• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Crossrefs

Square root of g.f. for A054552.

Programs

Magma

m:=40; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!(Sqrt((1-x+8*x^2)/(1-x)^3))); // Vincenzo Librandi, Jan 25 2020

Mathematica

CoefficientList[Series[Sqrt[(1-x+8x^2)/(1-x)^3],{x,0,50}],x] (* Harvey P. Dale, Dec 24 2018 *)

Formula

D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +(9*n-25)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jan 24 2020