

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.


2



1, 0, 8, 40, 312, 2240, 17280, 134568, 1071000, 8627872, 70302888, 577920200, 4786740112, 39899052960, 334391846048, 2815803070920, 23809393390680, 202061204197632, 1720404406215720, 14690717541313128, 125775000062934552
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OFFSET

0,3


COMMENTS

Also, cogrowth function of a certain group given by Humphries 1997 (page 211).


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Stephen P Humphries, Cogrowth of groups and the DedekindFrobenius group determinant, Mathematical Proc. Camb. Phil. Soc. (1997) vol. 121, pp. 193217


FORMULA

For n>0, a(n) = A168597(n)  A168597(n1) = A002426(n)^2  A002426(n1)^2.
G.f.: (1x)*hypergeom([1/12, 5/12],[1],1728*x^4*(x1)*(9*x1)*(3*x+1)^2/(81*x^436*x^326*x^24*x+1)^3)/(81*x^436*x^326*x^24*x+1)^(1/4).  Mark van Hoeij, Apr 10 2014


MATHEMATICA

CoefficientList[Series[(1  x)*Hypergeometric2F1[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), {x, 0, 50}], x] (* G. C. Greubel, Mar 07 2017 *)


CROSSREFS

Sequence in context: A188332 A158922 A117083 * A096969 A209829 A209848
Adjacent sequences: A007984 A007985 A007986 * A007988 A007989 A007990


KEYWORD

nonn


AUTHOR

Stephen P. Humphries


EXTENSIONS

Formula and further terms from Max Alekseyev, Jun 04 2011


STATUS

approved



