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%I #17 Mar 11 2022 04:44:11
%S 1,0,21,136,465,1176,2485,4656,8001,12880,19701,28920,41041,56616,
%T 76245,100576,130305,166176,208981,259560,318801,387640,467061,558096,
%U 661825,779376,911925,1060696,1226961
%N a(n) = (n^2-1)*(2*n^2-1).
%H G. C. Greubel, <a href="/A033595/b033595.txt">Table of n, a(n) for n = 0..1000</a>
%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.: (1 -5*x +31*x^2 +21*x^3)/(1-x)^5. - _R. J. Mathar_, Feb 06 2017
%F E.g.f.: (1 - x + 11*x^2 + 12*x^3 + 2*x^4)*exp(x). - _G. C. Greubel_, Mar 05 2020
%F From _Amiram Eldar_, Mar 11 2022: (Start)
%F Sum_{n>=2} 1/a(n) = (Pi/sqrt(2))*cot(Pi/sqrt(2)) + 7/4.
%F Sum_{n>=2} (-1)^n/a(n) = (Pi/sqrt(2))*cosec(Pi/sqrt(2)) - 11/4. (End)
%p seq( (n^2 -1)*(2*n^2 -1), n=0..40); # _G. C. Greubel_, Mar 05 2020
%t Table[(n^2 -1)*(2*n^2 -1), {n,0,40}] (* _G. C. Greubel_, Mar 05 2020 *)
%t LinearRecurrence[{5,-10,10,-5,1},{1,0,21,136,465},40] (* _Harvey P. Dale_, Aug 24 2020 *)
%o (PARI) vector(41, n, my(m=n-1); (m^2 -1)*(2*m^2 -1)) \\ _G. C. Greubel_, Mar 05 2020
%o (Magma) [(n^2 -1)*(2*n^2 -1): n in [0..40]]; // _G. C. Greubel_, Mar 05 2020
%o (Sage) [(n^2 -1)*(2*n^2 -1) for n in (0..40)] # _G. C. Greubel_, Mar 05 2020
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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