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%I #24 May 07 2024 06:37:37
%S -1,9,35,77,135,209,299,405,527,665,819,989,1175,1377,1595,1829,2079,
%T 2345,2627,2925,3239,3569,3915,4277,4655,5049,5459,5885,6327,6785,
%U 7259,7749,8255,8777,9315,9869,10439,11025,11627,12245,12879,13529,14195,14877,15575,16289,17019,17765
%N a(n) = (2*n+1) * (4*n-1).
%H G. C. Greubel, <a href="/A033566/b033566.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A005408(n) * A004767(n-1). - _Michel Marcus_, Oct 03 2016
%F From _G. C. Greubel_, Oct 12 2019: (Start)
%F G.f.: (-1 + 12*x + 5*x^2)/(1-x)^3.
%F E.g.f.: (-1 + 10*x + 8*x^2)*exp(x). (End)
%F Sum_{n>=0} 1/a(n) = -2/3 +log(2)/6-Pi/12 = -0.81294152437.. - _R. J. Mathar_, May 07 2024
%p seq((2*n+1)*(4*n-1), n=0..50); # _G. C. Greubel_, Oct 12 2019
%t Table[(2*n+1)*(4*n-1), {n, 0, 50}] (* _G. C. Greubel_, Oct 12 2019 *)
%o (PARI) a(n) = (2*n+1) * (4*n-1); \\ _Michel Marcus_, Oct 03 2016
%o (Magma) [(2*n+1)*(4*n-1): n in [0..50]] # _G. C. Greubel_, Oct 12 2019
%o (Sage) [(2*n+1)*(4*n-1) for n in range(50)] # _G. C. Greubel_, Oct 12 2019
%o (GAP) List([0..50], n-> (2*n+1)*(4*n-1)); # _G. C. Greubel_, Oct 12 2019
%Y Cf. A004767, A005408.
%K sign,easy,changed
%O 0,2
%A _N. J. A. Sloane_
%E Terms a(37) onward added by _G. C. Greubel_, Oct 12 2019
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