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%I #17 Apr 26 2021 21:39:05
%S 945,36465,229425,801009,2070705,4456305,8473905,14737905,23961009,
%T 36954225,54626865,77986545,108139185,146289009,193738545,251888625,
%U 322238385,406385265,506025009,622951665,759057585,916333425,1096868145
%N a(n) = (8*n+3)*(8*n+5)*(8*n+7)*(8*n+9).
%C Also 1/3-1/5-1/7+1/9+1/11-1/13-1/15+1/17+1/19--++... = Pi*sqrt(2)/4-1 - _Miklos Kristof_, Sep 15 2008
%C Also sum(2*(-1)^n/((4*n+3)*(4*n+5)), n=0..infinity) = Pi*sqrt(2)/4-1 - _Miklos Kristof_, Sep 15 2008
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: 3*(315 + 10580*x + 18850*x^2 + 3028*x^3 - 5*x^4)/(1-x)^5.
%F E.g.f: (945 + 35520*x + 78720*x^2 + 36864*x^3 + 4096*x^4)*exp(x).
%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Apr 26 2021
%p seq((8*n+3)*(8*n+5)*(8*n+7)*(8*n+9), n=0..30);
%p sum(32*(4*n+3)/((8*n+3)*(8*n+5)*(8*n+7)*(8*n+9)), n=0..infinity) = Pi*sqrt(2)/4-1. Maple: evalf(Pi*sqrt(2)/4-1, 30); gives 0.11072073453959156175397024752... - _Miklos Kristof_, Sep 15 2008
%t Times@@@(#+{3,5,7,9}&/@(8Range[0,25])) (* _Harvey P. Dale_, Mar 14 2011 *)
%K nonn,easy
%O 0,1
%A _Miklos Kristof_, Jan 06 2008, Sep 15 2008
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