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 A008487 #61 Sep 08 2022 08:44:35
%S A008487 1,5,15,35,70,125,205,315,460,645,875,1155,1490,1885,2345,2875,3480,
%T A008487 4165,4935,5795,6750,7805,8965,10235,11620,13125,14755,16515,18410,
%U A008487 20445,22625,24955,27440,30085,32895,35875,39030,42365,45885,49595,53500,57605,61915
%N A008487 Expansion of (1-x^5) / (1-x)^5.
%C A008487 Related to the 4-dimensional cyclotomic lattice Z[zeta_5] (or A_4^{*}).
%C A008487 Growth series of the affine Weyl group of type A4. - _Paul E. Gunnells_, Jan 06 2017
%D A008487 R. Bott, The geometry and the representation theory of compact Lie groups, in: Representation Theory of Lie Groups, in: London Math. Soc. Lecture Note Ser., vol. 34, Cambridge University Press, Cambridge, 1979, pp. 65-90.
%D A008487 J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 158.
%H A008487 Colin Barker, <a href="/A008487/b008487.txt">Table of n, a(n) for n = 0..1000</a>
%H A008487 M. Beck and S. Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.
%H A008487 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 A008487 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A008487 a(n) is the sum of 5 consecutive tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6 = A000292(n) for n>0, a(0) = 1. a(n) = A000292(n-4) + A000292(n-3) + A000292(n-2) + A000292(n-1) + A000292(n) for n>0, a(0) = 1. - _Alexander Adamchuk_, May 20 2006
%F A008487 Equals binomial transform of [1, 4, 6, 4, 1, -1, 1, -1, 1, ...]. - _Gary W. Adamson_, Apr 29 2008
%F A008487 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. - _Colin Barker_, Jan 06 2017
%F A008487 For n >= 1, a(n) = (5*n^3 + 25*n)/6. - _Christopher Hohl_, Dec 30 2018
%F A008487 E.g.f.: 1 + x*(30 + 15*x + 5*x^2)*exp(x)/6. - _G. C. Greubel_, Nov 07 2019
%p A008487 1, seq(5*n*(n^2 +5)/6, n=1..50); # _G. C. Greubel_, Nov 07 2019
%t A008487 CoefficientList[Series[(1-x^5)/(1-x)^5, {x, 0, 50}], x] (* _Stefano Spezia_, Dec 30 2018 *)
%o A008487 (PARI) Vec((1-x^5) / (1-x)^5+O(x^50)) \\ _Charles R Greathouse IV_, Sep 26 2012; corrected by _Colin Barker_, Jan 06 2017
%o A008487 (Magma) [1] cat [5*n*(n^2 +5)/6: n in [1..50]]; // _G. C. Greubel_, Nov 07 2019
%o A008487 (Sage) [1]+[5*n*(n^2 +5)/6 for n in (1..50)] # _G. C. Greubel_, Nov 07 2019
%o A008487 (GAP) concatenation([1], List([1..50], n-> 5*n*(n^2 +5)/6)); # _G. C. Greubel_, Nov 07 2019
%Y A008487 Cf. A000292, A008498, A008531, A222408.
%K A008487 nonn,easy
%O A008487 0,2
%A A008487 _N. J. A. Sloane_