A027635 Expansion of (1-x^8)*(1+x^5)/(1-x^2)^5.

1, 0, 5, 0, 15, 1, 35, 5, 69, 15, 121, 35, 195, 69, 295, 121, 425, 195, 589, 295, 791, 425, 1035, 589, 1325, 791, 1665, 1035, 2059, 1325, 2511, 1665, 3025, 2059, 3605, 2511, 4255, 3025, 4979, 3605, 5781, 4255, 6665, 4979, 7635, 5781, 8695, 6665, 9849, 7635, 11101, 8695, 12455, 9849, 13915

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

B. Runge, On Siegel modular forms II, Nagoya Math. J., 138 (1995), 179-197.

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

From Colin Barker, Aug 06 2013: (Start)

a(n) = (24*(-4 + 5*(-1)^n) + (73 - 45*(-1)^n)*n + 3*(-3 + 5*(-1)^n)*n^2 + 2*n^3)/24.

G.f.: (1+x^2)*(1-x+x^2-x^3+x^4)*(1+x^4) / ((1-x)^4*(1+x)^3). (End)

E.g.f.: 5*x + x^3/6 + (1/24)*(15*(8 + 2*x + x^2)*exp(-x) - (96 - 66*x + 3*x^2 - 2*x^3)*exp(x)). - G. C. Greubel, Aug 04 2022

Mathematica

CoefficientList[Series[(1-x^8)(1+x^5)/(1-x^2)^5, {x, 0, 60}], x] (* or *) Join[{1, 0, 5, 0}, LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {15, 1, 35, 5, 69, 15, 121}, 60]] (* Harvey P. Dale, Sep 21 2013 *)

Prog

(PARI) x='x+O('x^66); Vec((1-x^8)*(1+x^5)/(1-x^2)^5) \\ Joerg Arndt, Aug 06 2013
(Magma) [1, 0, 5, 0] cat [(24*(-4+5*(-1)^n)+(73-45*(-1)^n)*n+3*(-3+5*(-1)^n)*n^2 +2*n^3)/24: n in [4..60]]; // Vincenzo Librandi, Oct 18 2013
(SageMath) [((-1)^n*15*(8 -3*n +n^2) - (96 -73*n +9*n^2 -2*n^3))/24 + 5*bool(n==1) + bool(n==3) for n in (0..60)] # G. C. Greubel, Aug 04 2022

Crossrefs

Sequence in context: A024418 A167297 A290867 * A291218 A321416 A226372

Adjacent sequences: A027632 A027633 A027634 * A027636 A027637 A027638

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Aug 06 2013

Status

approved