%I #9 Nov 24 2016 09:37:52
%S 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T 615093750000,9226406250000,138396093749880,2075941406246400,
%U 31139121093669120,467086816404633600,7006302246063456000
%N Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A166584/b166584.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F G.f.: (t^12 + 2*t^11 + 2*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)/(105*t^12 - 14*t^11 - 14*t^10 - 14*t^9 -14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 -14*t +1).
%t CoefficientList[Series[(t^12 + 2*t^11 + 2*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)/(105*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 50}], t](* _G. C. Greubel_, May 17 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009