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 A085440 #31 Jan 13 2025 11:10:24
%S A085440 1,244,8020,108020,867395,4951496,22161864,82628040,267156165,
%T A085440 770440540,2022773116,4909947484,11150268935,23913084560,48796284560,
%U A085440 95322158736,179163294729,325374464580,572984364580,981394464580,1639143014731,2675722491224,4277290592600
%N A085440 a(n) = Sum_{i=1..n} binomial(i+1,2)^5.
%D A085440 Elisabeth Busser and Gilles Cohen, Neuro-Logies - "Chercher, jouer, trouver", La Recherche, April 1999, No. 319, page 97.
%H A085440 T. D. Noe, <a href="/A085440/b085440.txt">Table of n, a(n) for n = 1..1000</a>
%H A085440 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 A085440 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A085440 a(n) = (113400*n^11 +1247400*n^10 +5544000*n^9 +12474000*n^8 +14196600*n^7 +6237000*n^6 -831600*n^5 +1108800*n^3 -172800*n)/11!.
%F A085440 G.f.: x*(x^8+232*x^7+5158*x^6+27664*x^5+47290*x^4+27664*x^3+5158*x^2+232*x+1) / (x-1)^12. - _Colin Barker_, May 02 2014
%t A085440 Table[(113400*n^11 +1247400*n^10 +5544000*n^9 +12474000*n^8 +14196600*n^7 +6237000*n^6 -831600*n^5 +1108800*n^3 -172800*n)/11!, {n,1,50}] (* _G. C. Greubel_, Nov 22 2017 *)
%o A085440 (PARI) for(n=1,30, print1(sum(k=1,n, binomial(k+1,2)^5), ", ")) \\ _G. C. Greubel_, Nov 22 2017
%o A085440 (Magma) [(113400*n^11 +1247400*n^10 +5544000*n^9 +12474000*n^8 +14196600*n^7 +6237000*n^6 -831600*n^5 +1108800*n^3 -172800*n )/Factorial(11): n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y A085440 Column k=5 of A334781.
%Y A085440 Cf. A000292, A087127, A024166, A024166, A085438, A085439, A085441, A085442, A000332, A086020, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.
%K A085440 easy,nonn
%O A085440 1,2
%A A085440 _André F. Labossière_, Jun 30 2003
%E A085440 Formula edited by _Colin Barker_, May 02 2014