A008632 - OEIS

%I #20 Sep 08 2022 08:44:36

%S 1,1,2,3,5,7,11,15,22,30,41,54,73,94,123,157,201,252,318,393,488,598,

%T 732,887,1076,1291,1549,1845,2194,2592,3060,3589,4206,4904,5708,6615,

%U 7658,8825,10158,11651,13343,15231,17365,19735,22402,25361,28670

%N Molien series for A_9.

%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.

%H Sean A. Irvine, <a href="/A008632/b008632.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%H <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,-2,-1,-1,-1,2,0,1,3,-1,1,0,-3,0,-2,-1,1,-1,1,2,0,3,0,-1,1,-3,-1,0,-2,1,1,1,2,-1,0,-1,-1,1).

%F G.f.: (1+x^36)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)* (1-x^9)).

%p seq(coeff(series( (1+x^36)/mul((1-x^j), j=1..9)), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Feb 02 2020

%t CoefficientList[Series[(1+x^36)/Product[(1-x^j), {j,1,9}], {x,0,50}], x] (* _G. C. Greubel_, Feb 02 2020 *)

%o (PARI) Vec( (1+x^36)/prod(j=1,9, 1-x^j) +O('x^50) ) \\ _G. C. Greubel_, Feb 02 2020

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^36)/(&*[1-x^j: j in [1..9]]) )); // _G. C. Greubel_, Feb 02 2020

%o (Sage)

%o def A008631_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( (1+x^36)/product(1-x^j for j in (1..9)) ).list()

%o A008631_list(70) # _G. C. Greubel_, Feb 02 2020

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Apr 01 2018