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%I #23 Mar 20 2020 04:38:32
%S 1,1,2,3,5,7,11,14,20,26,35,44,58,71,90,111,137,165,202,240,289,342,
%T 405,474,558,647,753,869,1002,1147,1316,1496,1703,1928,2180,2454,2763,
%U 3093,3463,3863,4304,4779,5305,5866,6484,7148,7870,8644,9489,10387,11364
%N Molien series for A_6.
%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1,-2,-1,-1,2,2,2,-1,-1,-2,-1,1,1,1,-1).
%F G.f.: (1+x^15)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)).
%F a(n) ~ 1/43200*n^5 + 1/2880*n^4 + 17/8640*n^3. - _Ralf Stephan_, Apr 29 2014
%F G.f.: (1-x^3-x+x^2+x^4)*(x^8+x^7-x^5-x^4-x^3+x+1) / ( (x^2+1) *(1+x^3+x+x^2+x^4) *(1+x)^2 *(1+x+x^2)^2 *(x-1)^6 ). - _R. J. Mathar_, Dec 18 2014
%t LinearRecurrence[{1,1,1,-1,-2,-1,-1,2,2,2,-1,-1,-2,-1,1,1,1,-1},{1,1,2,3,5,7,11,14,20,26,35,44,58,71,90,111,137,165},51] (* _Ray Chandler_, Jul 15 2015 *)
%o (Sage)
%o ring = PowerSeriesRing(ZZ, 'x', default_prec=50)
%o ms = AlternatingGroup(6).molien_series()
%o list(ring(ms))
%o # _Ralf Stephan_, Apr 29 2014
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
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