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 A008389 #39 Aug 11 2024 23:24:08
%S A008389 1,56,812,5768,26474,91112,256508,623576,1356194,2703512,5025692,
%T A008389 8823080,14768810,23744840,36881420,55599992,81659522,117206264,
%U A008389 164826956,227605448,309182762,413820584,546468188,712832792,919453346
%N A008389 Coordination sequence for A_7 lattice.
%H A008389 T. D. Noe, <a href="/A008389/b008389.txt">Table of n, a(n) for n = 0..1000</a>
%H A008389 M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256.
%H A008389 R. Bacher, P. de la Harpe and B. Venkov, <a href="https://doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A008389 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A008389 M. O'Keeffe, <a href="http://dx.doi.org/10.1524/zkri.1995.210.12.905">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908.
%H A008389 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008389 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A008389 G.f.: (1+x)*(1+48*x+393*x^2+832*x^3+393*x^4+48*x^5+x^6)/(1-x)^7. - _Colin Barker_, Sep 26 2012
%F A008389 a(n) = 2 + n^2*(143*n^4 +770*n^2 +707)/30 with n>0, a(0)=1. - _Bruno Berselli_, Sep 26 2012
%F A008389 E.g.f.: -1 + (1/30)*(60 +1620*x +10530*x^2 +17490*x^3 +10065*x^4 +2145*x^5 +143*x^6)*exp(x). - _G. C. Greubel_, May 26 2023
%p A008389 1, seq(2 +n^2*(143*n^4 +770*n^2 +707)/30, n=1..50);
%t A008389 Table[n^2*(143*n^4 +770*n^2 +707)/30 +2 -Boole[n==0], {n,0,40}] (* _G. C. Greubel_, May 26 2023 *)
%o A008389 (Magma) [1] cat [2 +n^2*(143*n^4 +770*n^2 +707)/30: n in [1..40]]; // _G. C. Greubel_, May 26 2023
%o A008389 (SageMath) [2 +n^2*(143*n^4 +770*n^2 +707)/30 -int(n==0) for n in range(41)] # _G. C. Greubel_, May 26 2023
%Y A008389 Row 7 of A103881.
%K A008389 nonn,easy
%O A008389 0,2
%A A008389 _N. J. A. Sloane_ and _J. H. Conway_