A110689 Expansion of (2*x+1)*(4*x^2+8*x+1)/((3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)).

1, 3, -18, 63, -207, 696, -2415, 8565, -30714, 110583, -398439, 1435152, -5167083, 18598065, -66931314, 240862563, -866772819, 3119198160, -11224913079, 40394716341, -145367356794, 523129840335, -1882574375679, 6774773362320, -24380205972915

Offset: 0

Author

Creighton Dement, Aug 02 2005

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-7,-17,-20,-12,-6).

Crossrefs

Cf. A110687, A110688, A110679.

Programs

Maple

seriestolist(series((2*x+1)*(4*x^2+8*x+1)/((3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: tessum(infty)-4basekforsumseq[ + 'i - .25'j + .25'k - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e], Sumtype is set to: default; Fortype is set to: 1A.

Mathematica

CoefficientList[Series[(2*x + 1)*(4*x^2 + 8*x + 1)/((3*x^2 + 3*x + 1)*(2*x^3 + 2*x^2 + 4*x + 1)), {x, 0, 50}], x] (* G. C. Greubel, Sep 06 2017 *)

PARI

Vec((2*x+1)*(4*x^2+8*x+1)/((3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012