This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259317 #20 Jul 12 2025 10:47:29
%S A259317 0,2,70,588,2772,9438,26026,61880,131784,257754,471086,814660,1345500,
%T A259317 2137590,3284946,4904944,7141904,10170930,14202006,19484348,26311012,
%U A259317 35023758,46018170,59749032,76735960,97569290,122916222,153527220,190242668,233999782
%N A259317 a(n) = 2*(2*n+1)*A000538(n) - 4*A000330(n)^2.
%H A259317 Colin Barker, <a href="/A259317/b259317.txt">Table of n, a(n) for n = 0..1000</a>
%H A259317 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 A259317 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A259317 Also a(n) = (2*n+1)*A259108(n) - A006331(n)^2.
%F A259317 a(n) = (n*(1+2*n)^2*(-3+n+8*n^2+4*n^3))/45. - _Colin Barker_, Jun 28 2015
%F A259317 G.f.: -2*x*(x^4+28*x^3+70*x^2+28*x+1) / (x-1)^7. - _Colin Barker_, Jun 28 2015
%e A259317 n=3: 588 = 2*7*92-4*14^2.
%t A259317 LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,2,70,588,2772,9438,26026},30] (* _Harvey P. Dale_, Jul 12 2025 *)
%o A259317 (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 A259317 (Python)
%o A259317 def A259317(n): return n*(n*(n**2*(n*(16*n + 48) + 40) - 11) - 3)//45 # _Chai Wah Wu_, Dec 07 2021
%Y A259317 Cf. A000538, A000330, A006331, A259108, A259109, A259318.
%K A259317 nonn,easy
%O A259317 0,2
%A A259317 _N. J. A. Sloane_, Jun 24 2015