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%I #18 Dec 07 2021 20:12:54
%S 0,2,70,588,2772,9438,26026,61880,131784,257754,471086,814660,1345500,
%T 2137590,3284946,4904944,7141904,10170930,14202006,19484348,26311012,
%U 35023758,46018170,59749032,76735960,97569290,122916222,153527220,190242668,233999782
%N a(n) = 2*(2*n+1)*A000538(n) - 4*A000330(n)^2.
%H Colin Barker, <a href="/A259317/b259317.txt">Table of n, a(n) for n = 0..1000</a>
%H J. L. Bailey, Jr., <a href="http://dx.doi.org/10.1214/aoms/1177732978">A table to facilitate the fitting of certain logistic curves</a>, Annals Math. Stat., 2 (1931), 355-359.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F Also a(n) = (2*n+1)*A259108(n) - A006331(n)^2.
%F a(n) = (n*(1+2*n)^2*(-3+n+8*n^2+4*n^3))/45. - _Colin Barker_, Jun 28 2015
%F G.f.: -2*x*(x^4+28*x^3+70*x^2+28*x+1) / (x-1)^7. - _Colin Barker_, Jun 28 2015
%e n=3: 588 = 2*7*92-4*14^2.
%o (PARI) concat(0, Vec(-2*x*(x^4+28*x^3+70*x^2+28*x+1)/(x-1)^7 + O(x^100))) \\ _Colin Barker_, Jun 28 2015
%o (Python)
%o def A259317(n): return n*(n*(n**2*(n*(16*n + 48) + 40) - 11) - 3)//45 # _Chai Wah Wu_, Dec 07 2021
%Y Cf. A000538, A000330, A006331, A259108, A259109, A259318.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jun 24 2015
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