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%I #30 Mar 08 2017 02:26:57
%S 1,0,8,40,312,2240,17280,134568,1071000,8627872,70302888,577920200,
%T 4786740112,39899052960,334391846048,2815803070920,23809393390680,
%U 202061204197632,1720404406215720,14690717541313128,125775000062934552
%N Number of irreducible words of length 2n in the free group with generators x,y such that the total degree of x and the total degree of y both equal zero.
%C Also, co-growth function of a certain group given by Humphries 1997 (page 211).
%H G. C. Greubel, <a href="/A007987/b007987.txt">Table of n, a(n) for n = 0..1000</a>
%H Stephen P Humphries, <a href="http://dx.doi.org/10.1017/S030500419600134X">Cogrowth of groups and the Dedekind-Frobenius group determinant</a>, Mathematical Proc. Camb. Phil. Soc. (1997) vol. 121, pp. 193-217
%F For n>0, a(n) = A168597(n) - A168597(n-1) = A002426(n)^2 - A002426(n-1)^2.
%F G.f.: (1-x)*hypergeom([1/12, 5/12],[1],1728*x^4*(x-1)*(9*x-1)*(3*x+1)^2/(81*x^4-36*x^3-26*x^2-4*x+1)^3)/(81*x^4-36*x^3-26*x^2-4*x+1)^(1/4). - _Mark van Hoeij_, Apr 10 2014
%t CoefficientList[Series[(1 - x)*Hypergeometric2F1[1/12, 5/12, 1,
%t 1728*x^4*(x - 1)*(9*x - 1)*(3*x + 1)^2/(81*x^4 - 36*x^3 - 26*x^2 - 4*x + 1)^3]/(81*x^4 - 36*x^3 - 26*x^2 - 4*x + 1)^(1/4), {x, 0,50}], x] (* _G. C. Greubel_, Mar 07 2017 *)
%K nonn
%O 0,3
%A _Stephen P. Humphries_
%E Formula and further terms from _Max Alekseyev_, Jun 04 2011
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