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 A008402 #40 Dec 10 2023 16:09:23
%S A008402 1,55,883,6085,26461,86491,232975,545833,1151065,2235871,4065931,
%T A008402 7004845,11535733,18284995,28048231,41818321,60815665,86520583,
%U A008402 120707875,165483541,223323661,297115435
%N A008402 Crystal ball sequence for {E_6}* lattice.
%D A008402 M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H A008402 T. D. Noe, <a href="/A008402/b008402.txt">Table of n, a(n) for n = 0..1000</a>
%H A008402 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 A008402 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 A008402 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008402 <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>
%H A008402 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A008402 G.f.: (1 + 48*x + 519*x^2 + 1024*x^3 + 519*x^4 + 48*x^5 + x^6)/(1-x)^7.
%F A008402 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=1, a(1)=55, a(2)=883, a(3)=6085, a(4)=26461, a(5)=86491, a(6)=232975. - _Harvey P. Dale_, Jun 20 2013
%F A008402 a(n) = 3*n^6 + 9*n^5 + 15*n^4 + 15*n^3 + 9*n^2 + 3*n + 1 = 1 + 3*n*(n+1)*(n^2+n+1)^2. - _Charles R Greathouse IV_, Jun 20 2013
%F A008402 E.g.f.: exp(x)*(1 + 54*x + 387*x^2 + 600*x^3 + 300*x^4 + 54*x^5 + 3*x^6). - _Stefano Spezia_, Apr 15 2022
%t A008402 CoefficientList[Series[(1+48x+519x^2+1024x^3+519x^4+48x^5+x^6)/(1-x)^7,{x,0,30}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,55, 883,6085,26461,86491,232975},30] (* _Harvey P. Dale_, Jun 20 2013 *)
%o A008402 (PARI) 3*n^6+9*n^5+15*n^4+15*n^3+9*n^2+3*n+1 \\ _Charles R Greathouse IV_, Jun 20 2013
%o A008402 (Magma) [1 +3*n*(n+1)*(n^2+n+1)^2: n in [0..40]]; // _G. C. Greubel_, May 31 2023
%o A008402 (SageMath) [1 +3*n*(n+1)*(n^2+n+1)^2 for n in range(41)] # _G. C. Greubel_, May 31 2023
%Y A008402 Partial sums of A008401.
%K A008402 nonn,nice,easy
%O A008402 0,2
%A A008402 _N. J. A. Sloane_