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%I #18 Sep 08 2022 08:44:59
%S 1,15,95,374,1105,2701,5775,11180,20049,33835,54351,83810,124865,
%T 180649,254815,351576,475745,632775,828799,1070670,1366001,1723205,
%U 2151535,2661124,3263025,3969251,4792815,5747770,6849249,8113505
%N a(n) = n*(2*n^2 + 1)*(n^2 + 1)/6.
%C 2-magic series constant.
%H G. C. Greubel, <a href="/A052459/b052459.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MagicConstant.html">Magic constant.</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: x*(1 + 3*x + x^2)*(1 + 6*x + x^2)/(1-x)^6. - _Chai Wah Wu_, Dec 17 2016
%F E.g.f.: x*(6 +39*x +53*x^2 +20*x^3 +2*x^4)*exp(x)/6. - _G. C. Greubel_, Sep 23 2019
%p seq(n*(2*n^2 +1)*(n^2 +1)/6, n=1..30); # _G. C. Greubel_, Sep 23 2019
%t Table[n*(2*n^2 +1)*(n^2 +1)/6, {n, 30}] (* _G. C. Greubel_, Sep 23 2019 *)
%o (PARI) vector(30, n, n*(2*n^2 +1)*(n^2 +1)/6) \\ _G. C. Greubel_, Sep 23 2019
%o (Magma) [n*(2*n^2 +1)*(n^2 +1)/6: n in [1..30]]; // _G. C. Greubel_, Sep 23 2019
%o (Sage) [n*(2*n^2 +1)*(n^2 +1)/6 for n in (1..30)] # _G. C. Greubel_, Sep 23 2019
%o (GAP) List([1..30], n-> n*(2*n^2 +1)*(n^2 +1)/6); # _G. C. Greubel_, Sep 23 2019
%Y Cf. A052460, A052461.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_
%E Formula from _Vladeta Jovovic_, Jun 15 2002
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