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 A266785 #20 Feb 12 2024 13:27:08
%S A266785 1,8,35,112,294,673,1393,2668,4803,8218,13476,21315,32684,48782,71101,
%T A266785 101473,142121,195714,265426,354999,468809,611936,790238,1010430,
%U A266785 1280166,1608124,2004094,2479071,3045353,3716642,4508148,5436696,6520838,7780968,9239441,10920695,12851378,15060479,17579463,20442410,23686158,27350450,31478083
%N A266785 The growth series for the affine Weyl group E_7.
%D A266785 N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t).
%D A266785 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
%D A266785 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial; also Table 3.1 page 59.
%H A266785 G. C. Greubel, <a href="/A266785/b266785.txt">Table of n, a(n) for n = 0..1000</a>
%H A266785 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 1, -4, 7, -8, 7, -4, 2, -4, 6, -4, 1, 0, 0, -1, 4, -6, 4, -2, 4, -7, 8, -7, 4, -1, 0, 0, 0, 0, 0, 0, 1, -4, 6, -4, 1).
%F A266785 G.f.: (1 +t)*(1 +t^3)*(1 +t^5)*(1 +t^7)*(1 +t +t^2 +t^3 +t^4 +t^5 +t^6 +t^7)*(1 +t +t^2 +t^9 +t^10 +t^11)*(1 +t +t^2 +t^3 +t^4 +t^5 +t^6 +t^7 +t^8 +t^9 +t^10 +t^11)/((1-t)^4*(1-t^11)*(1-t^13)*(1-t^17)).
%F A266785 G.f.: ((1-x^2)*(1-x^18)/((1-x)^8*(1-x^17)))*Product_{j=0..4} (1-x^(2*j+6))/(1-x^(2*j+5)). - _G. C. Greubel_, Feb 05 2020
%p A266785 m:=45; S:=series(((1-x^2)*(1-x^18)/((1-x)^8*(1-x^17)))*mul((1-x^(2*j+6))/(1-x^(2*j+5)), j=0..4)), x, m+1): seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Feb 04 2020
%t A266785 CoefficientList[Series[((1-x^2)*(1-x^18)/((1-x)^8*(1-x^17)))*Product[(1-x^(2*j + 6))/(1-x^(2*j+5)), {j,0,4}], {x,0,45}], x] (* _G. C. Greubel_, Feb 04 2020 *)
%o A266785 (PARI) Vec( ((1-x^2)*(1-x^18)/((1-x)^8*(1-x^17)))*prod(j=0,4, (1-x^(2*j+6))/(1-x^(2*j+5))) +O('x^45) ) \\ _G. C. Greubel_, Feb 04 2020
%o A266785 (Magma) R<x>:=PowerSeriesRing(Integers(), 45); Coefficients(R!( ((1-x^2)*(1-x^18)/((1-x)^8*(1-x^17)))*(&*[(1-x^(2*j+6))/(1-x^(2*j+5)): j in [0..4]]) )); // _G. C. Greubel_, Feb 04 2020
%o A266785 (Sage)
%o A266785 def A266785_list(prec):
%o A266785 P.<x> = PowerSeriesRing(ZZ, prec)
%o A266785 return P( ((1-x^2)*(1-x^18)/((1-x)^8*(1-x^17)))*product((1-x^(2*j+6))/(1-x^(2*j+5)) for j in (0..4)) ).list()
%o A266785 A266785_list(45) # _G. C. Greubel_, Feb 04 2020
%Y A266785 For the growth series for the finite group see A162493.
%K A266785 nonn
%O A266785 0,2
%A A266785 _N. J. A. Sloane_, Jan 11 2016