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A166225 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166225 #14 Mar 11 2020 18:24:50
%S A166225 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A166225 6717440000000,268697600000000,10747903999999180,429916159999934400,
%U A166225 17196646399996064820,687865855999790145600,27514634239989507936000
%N A166225 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166225 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A166225 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166225 G. C. Greubel, <a href="/A166225/b166225.txt">Table of n, a(n) for n = 0..500</a>
%H A166225 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A166225 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)/(780*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
%p A166225 seq(coeff(series((1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166225 CoefficientList[Series[(1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 07 2016 *)
%t A166225 coxG[{10,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 30 2018 *)
%o A166225 (Sage)
%o A166225 def A166225_list(prec):
%o A166225     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166225     return P( (1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11) ).list()
%o A166225 A166225_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166225 nonn
%O A166225 0,2
%A A166225 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009