cp's OEIS Frontend

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.

A007987 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.

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%I A007987 #30 Mar 08 2017 02:26:57
%S A007987 1,0,8,40,312,2240,17280,134568,1071000,8627872,70302888,577920200,
%T A007987 4786740112,39899052960,334391846048,2815803070920,23809393390680,
%U A007987 202061204197632,1720404406215720,14690717541313128,125775000062934552
%N A007987 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 A007987 Also, co-growth function of a certain group given by Humphries 1997 (page 211).
%H A007987 G. C. Greubel, <a href="/A007987/b007987.txt">Table of n, a(n) for n = 0..1000</a>
%H A007987 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 A007987 For n>0, a(n) = A168597(n) - A168597(n-1) = A002426(n)^2 - A002426(n-1)^2.
%F A007987 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 A007987 CoefficientList[Series[(1 - x)*Hypergeometric2F1[1/12, 5/12, 1,
%t A007987 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 A007987 nonn
%O A007987 0,3
%A A007987 _Stephen P. Humphries_
%E A007987 Formula and further terms from _Max Alekseyev_, Jun 04 2011