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%I #18 Oct 17 2024 08:27:14
%S 0,36,300,1176,3240,7260,14196,25200,41616,64980,97020,139656,195000,
%T 265356,353220,461280,592416,749700,936396,1155960,1412040,1708476,
%U 2049300,2438736,2881200,3381300,3943836,4573800,5276376,6056940,6921060,7874496,8923200,10073316,11331180,12703320,14196456,15817500,17573556,19471920,21520080
%N Let T(n) = n(n+1)/2 be the n-th triangular number (A000217); a(n) = T(8T(n)).
%D C. Alsina and R. B. Nelson, Charming Proofs: A Journey into Elegant Mathematics, MAA, 2010. See p. 4.
%H G. C. Greubel, <a href="/A185096/b185096.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 From _G. C. Greubel_, Jun 22 2017: (Start)
%F a(n) = 2*n*(n + 1)*(2*n + 1)^2.
%F G.f.: 12*x*(3 + 10*x + 3*x^2)/(1 - x)^5.
%F E.g.f.: 2*x*(18 + 57*x + 32*x^2 + 4*x^3)*exp(x). (End)
%t Table[2*n*(n + 1)*(2*n + 1)^2, {n, 0, 50}] (* _G. C. Greubel_, Jun 22 2017 *)
%o (PARI) for(n=0,50, print1(2*n*(n+1)*(2*n+1)^2, ", ")) \\ _G. C. Greubel_, Jun 22 2017
%Y Cf. A000217, A185097.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 18 2011