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A027635 Expansion of (1-x^8)*(1+x^5)/(1-x^2)^5. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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

LINKS

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

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

FORMULA

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.: (x^2+1)*(x^4-x^3+x^2-x+1)*(x^4+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Aug 06 2013

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

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

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Last modified June 25 12:00 EDT 2019. Contains 324352 sequences. (Running on oeis4.)