A008628 - OEIS

%I #25 Mar 20 2020 04:38:16

%S 1,1,2,3,5,7,10,13,18,23,31,38,49,60,75,91,111,132,159,187,222,258,

%T 302,348,403,461,528,599,681,767,866,969,1086,1209,1347,1492,1653,

%U 1822,2009,2205,2421,2646,2893,3151,3432,3726,4044,4376,4735,5109,5512,5931

%N Molien series for A_5.

%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_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,0,1,-1,0,2,1,-2,-1,1).

%F a(n) ~ 1/1440*n^4 + 1/144*n^3. - _Ralf Stephan_, Apr 29 2014

%F G.f.: ( -1+x^2-x^4+x^6-x^8 ) / ( (1+x+x^2)*(1+x+x^2+x^3+x^4)*(1+x)^2*(x-1)^5 ). - _R. J. Mathar_, Dec 18 2014

%p (1+x^10)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5): seq(coeff(series(%,x,n+1),x,n), n=0..60);

%t LinearRecurrence[{1,2,-1,-2,0,1,-1,0,2,1,-2,-1,1},{1,1,2,3,5,7,10,13,18,23,31,38,49},52] (* _Ray Chandler_, Jul 15 2015 *)

%o (Sage)

%o ring = PowerSeriesRing(ZZ, 'x', default_prec=50)

%o ms = AlternatingGroup(5).molien_series()

%o list(ring(ms))

%o # _Ralf Stephan_, Apr 29 2014

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_.