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A166172 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166172 #14 Mar 11 2020 18:10:37
%S A166172 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A166172 5489240267160,214080370419240,8349134446349580,325616243407603200,
%U A166172 12699033492895339200,495262306222871990400,19315229942690204328000
%N A166172 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166172 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A166172 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166172 G. C. Greubel, <a href="/A166172/b166172.txt">Table of n, a(n) for n = 0..500</a>
%H A166172 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, -741).
%F A166172 G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
%p A166172 seq(coeff(series((1+t)*(1-t^10)/(1-39*t+779*t^10-741*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166172 CoefficientList[Series[(1+t)*(1-t^10)/(1-39*t+779*t^10-741*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 06 2016 *)
%t A166172 coxG[{10,741,-38}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 31 2017 *)
%o A166172 (Sage)
%o A166172 def A163878_list(prec):
%o A166172     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166172     return P( (1+t)*(1-t^10)/(1-39*t+779*t^10-741*t^11) ).list()
%o A166172 A163878_list(30) # _G. C. Greubel_, Aug 10 2019
%K A166172 nonn
%O A166172 0,2
%A A166172 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009