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 A008583 #45 Jul 26 2024 11:39:26
%S A008583 1,1,1,2,3,4,6,8,10,14,18,22,29,36,44,55,67,80,98,117,138,165,194,226,
%T A008583 266,309,356,413,475,542,622,708,802,911,1029,1157,1304,1462,1633,
%U A008583 1827,2036,2261,2514,2785
%N A008583 Molien series for Weyl group E_7.
%C A008583 The relevant generating function 1/((1-z^2)*(1-z^6)*(1-z^8)*(1-z^10)*(1-z^12)*(1-z^14)*(1-z^18)) is reduced with z^2=x below to indicate that the intermediate zeros are not stored in this sequence.
%D A008583 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, Ergebnisse der Mathematik und Ihrer Grenzgebiete, New Series, no. 14. Springer Verlag, 1957, Table 10.
%D A008583 L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 36).
%H A008583 T. D. Noe, <a href="/A008583/b008583.txt">Table of n, a(n) for n = 0..1000</a>
%H A008583 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=250">Encyclopedia of Combinatorial Structures 250</a>
%H A008583 Tengiz O. Gogoberidze, <a href="https://arxiv.org/abs/2407.12047">Baker's dozen digits of two sums involving reciprocal products of an integer and its greatest prime factor</a>, arXiv:2407.12047 [math.GM], 2024. See p. 6.
%H A008583 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A008583 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 0, 2, 0, 1, 0, 0, -1, 0, -2, 0, -1, 0, 1, 0, 1, 1, 0, 0, 0, -1, 0, -1, 1).
%F A008583 G.f.: 1/((1-x)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^9)).
%p A008583 A008583_list := proc(n) local G,j;
%p A008583 G:= series(1/((1-x)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^9)),x,n+1);
%p A008583 [seq(coeff(G,x,j),j=0..n)];
%p A008583 end proc; # _Robert Israel_, Mar 26 2012
%t A008583 CoefficientList[Series[1/((1-x)(1-x^3)(1-x^4)(1-x^5)(1-x^6)(1-x^7)(1-x^9)),{x,0,50}],x] (* _Harvey P. Dale_, Mar 04 2013 *)
%o A008583 (Magma) MolienSeries(CoxeterGroup("E7")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
%o A008583 (PARI) A008583_list(n)=Vec(1/((1-x)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^9))+O(x^n)) /* returns n terms [a(0),...,a(n-1)] */ \\ _M. F. Hasler_, Mar 26 2012
%o A008583 (Sage)
%o A008583 def A008583_list(n) :
%o A008583 R.<t> = PowerSeriesRing(ZZ)
%o A008583 G = 1/((1-t)*(1-t^3)*(1-t^4)*(1-t^5)*(1-t^6)*(1-t^7)*(1-t^9) + O(t^n))
%o A008583 return G.padded_list() # _Peter Luschny_, Mar 27 2012
%Y A008583 Cf. A005795.
%K A008583 nonn,easy,nice
%O A008583 0,4
%A A008583 _N. J. A. Sloane_