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 A086027 #31 Jan 14 2025 10:39:05
%S A086027 1,50,834,7890,51990,265434,1119210,4063866,13081875,38131900,
%T A086027 102259964,255425340,600047436,1336192860,2838530460,5783112156,
%U A086027 11350211925,21540508734,39656591950,71021001950,124026854850,211648774950,353581802550,579225802950,931794553575
%N A086027 a(n) = Sum_{i=1..n} binomial(i+5,6)^2.
%H A086027 T. D. Noe, <a href="/A086027/b086027.txt">Table of n, a(n) for n = 1..1000</a>
%H A086027 John Engbers and Christopher Stocker, <a href="http://epublications.marquette.edu/mscs_fac/456/">Two Combinatorial Proofs of Identities Involving Sums of Powers of Binomial Coefficients</a>, Integers 16 (2016), #A58.
%H A086027 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 A086027 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).
%F A086027 From _R. J. Mathar_, Jun 16 2010: (Start)
%F A086027 G.f.: x*(1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)/(1-x)^14.
%F A086027 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(77*n^6 + 1386*n^5 + 9380*n^4 + 29400*n^3 + 41783*n^2 + 20874*n + 60)/518918400. (End)
%p A086027 A086027:=n->sum(binomial(i+5,6)^2, i=1..n); seq(A086027(k), k=1..50); # _Wesley Ivan Hurt_, Oct 24 2013
%t A086027 Table[Sum[Binomial[k + 5, 6]^2, {k, 1, n}], {n, 50}] (* _Wesley Ivan Hurt_, Oct 24 2013 *)
%o A086027 (PARI) vector(30, n, sum(i=1,n, binomial(i+5,6)^2) ) \\ _G. C. Greubel_, Nov 22 2017
%o A086027 (Magma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(77*n^6 +1386*n^5 +9380*n^4 + 29400*n^3 +41783*n^2 +20874*n +60)/518918400: n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%o A086027 (Sage) [sum(binomial(j+5,6)^2 for j in (1..n)) for n in (1..30)] # _G. C. Greubel_, Aug 27 2019
%o A086027 (GAP) List([1..30], n-> Sum([1..n], j-> Binomial(j+5,6)^2)); # _G. C. Greubel_, Aug 27 2019
%Y A086027 Cf. A087127, A024166, A085438, A085439, A085440, A085441, A085442, A086020, A086021, A086022, A086023, A086024, A086025, A086026, A086028, A086029, A086030.
%K A086027 easy,nonn
%O A086027 1,2
%A A086027 _André F. Labossière_, Jul 11 2003
%E A086027 More terms from _R. J. Mathar_, Jun 16 2010