A110687 Expansion of -(7*x^2+3*x-1)*(2*x^2+2*x+1) / ((3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)).

1, -8, 28, -100, 358, -1276, 4558, -16342, 58732, -211306, 760498, -2737168, 9851098, -35452510, 127584124, -459135130, 1652275834, -5945992576, 21397667026, -77003195254, 277109379628, -997226422690, 3588693361378, -12914539595584, 46475225095450

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. A110688, A110689, A110679.

Programs

Maple

seriestolist(series(-(7*x^2+3*x-1)*(2*x^2+2*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[-(7*x^2 + 3*x - 1)*(2*x^2 + 2*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(-(7*x^2+3*x-1)*(2*x^2+2*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

Formula

a(n) = -7*a(n-1) - 17*a(n-2) - 20*a(n-3) - 12*a(n-4) - 6*a(n-5) for n>4. - Colin Barker, May 19 2019