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%I #29 Aug 08 2022 17:10:47
%S 1,0,5,0,15,1,35,5,69,15,121,35,195,69,295,121,425,195,589,295,791,
%T 425,1035,589,1325,791,1665,1035,2059,1325,2511,1665,3025,2059,3605,
%U 2511,4255,3025,4979,3605,5781,4255,6665,4979,7635,5781,8695,6665,9849,7635,11101,8695,12455,9849,13915
%N Expansion of (1-x^8)*(1+x^5)/(1-x^2)^5.
%H Vincenzo Librandi, <a href="/A027635/b027635.txt">Table of n, a(n) for n = 0..1000</a>
%H B. Runge, <a href="http://projecteuclid.org/euclid.nmj/1118775400">On Siegel modular forms II</a>, Nagoya Math. J., 138 (1995), 179-197.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F From _Colin Barker_, Aug 06 2013: (Start)
%F a(n) = (24*(-4 + 5*(-1)^n) + (73 - 45*(-1)^n)*n + 3*(-3 + 5*(-1)^n)*n^2 + 2*n^3)/24.
%F G.f.: (1+x^2)*(1-x+x^2-x^3+x^4)*(1+x^4) / ((1-x)^4*(1+x)^3). (End)
%F 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
%t 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 *)
%o (PARI) x='x+O('x^66); Vec((1-x^8)*(1+x^5)/(1-x^2)^5) \\ _Joerg Arndt_, Aug 06 2013
%o (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
%o (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
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Colin Barker_, Aug 06 2013
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