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 A085439 #27 Jan 13 2025 11:10:19
%S A085439 1,82,1378,11378,62003,256484,871140,2550756,6651381,15802006,
%T A085439 34776742,71791798,140366759,261917384,469277384,811379400,1359360681,
%U A085439 2214396762,3517606762,5462416762,8309813083,12406965164,18209748140,26309748140,37466388765,52644875166
%N A085439 a(n) = Sum_{i=1..n} binomial(i+1,2)^4.
%H A085439 G. C. Greubel, <a href="/A085439/b085439.txt">Table of n, a(n) for n = 1..5000</a>
%H A085439 Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 13.
%H A085439 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A085439 a(n) = (2520*n^9 +22680*n^8 +79920*n^7 +136080*n^6 +107352*n^5 +22680*n^4 -10080*n^3 +1728*n)/9!.
%F A085439 G.f.: x*(x^6+72*x^5+603*x^4+1168*x^3+603*x^2+72*x+1) / (x-1)^10. - _Colin Barker_, May 02 2014
%e A085439 a(15) = (2520*(15^9) +22680*(15^8) +79920*(15^7) +136080*(15^6) +107352*(15^5) +22680*(15^4) -10080*(15^3) +1728*15)/9! = 469277384.
%t A085439 Table[(2520*(n^9) + 22680*(n^8) + 79920*(n^7) + 136080*(n^6) + 107352*(n^5) + 22680*(n^4) - 10080*(n^3) + 1728*n)/9!, {n, 1, 50}] (* _G. C. Greubel_, Nov 22 2017 *)
%o A085439 (PARI) Vec(x*(x^6+72*x^5+603*x^4+1168*x^3+603*x^2+72*x+1)/(x-1)^10 + O(x^100)) \\ _Colin Barker_, May 02 2014
%o A085439 (PARI) a(n) = sum(i=1, n, binomial(i+1, 2)^4); \\ _Michel Marcus_, Nov 22 2017
%o A085439 (Magma) [(2520*n^9 +22680*n^8 +79920*n^7 +136080*n^6 +107352*n^5 +22680*n^4 -10080*n^3 +1728*n)/Factorial(9): n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y A085439 Column k=4 of A334781.
%Y A085439 Cf. A000292, A087127, A024166, A024166, A085438, A085440, A085441, A085442, A000332, A086020, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.
%K A085439 easy,nonn
%O A085439 1,2
%A A085439 _André F. Labossière_, Jul 03 2003
%E A085439 More terms from _Colin Barker_, May 02 2014
%E A085439 Typo in example fixed by _Colin Barker_, May 02 2014