A008635 - OEIS

%I #22 Sep 08 2022 08:44:36

%S 1,1,2,3,5,7,11,15,22,30,42,56,77,100,133,172,224,285,366,460,582,725,

%T 905,1116,1380,1686,2063,2503,3036,3655,4401,5262,6290,7476,8877,

%U 10489,12384,14552,17084,19978,23334,27156,31570,36578,42333,48849

%N Molien series for alternating group Alt_12 (or A_12).

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

%H Sean A. Irvine, <a href="/A008635/b008635.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_72">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 1, -2, -1, 0, 0, 1, 0, 1, 1, 2, 1, 0, 0, -1, -2, -3, -3, -1, -1, 1, 0, 3, 4, 3, 3, 1, 2, -2, -3, -3, -4, -3, -3, -2, 2, 1, 3, 3, 4, 3, 0, 1, -1, -1, -3, -3, -2, -1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, -1, -2, 1, -1, 0, 0, 1, 1, -1).

%F G.f.: (1+x^66)/((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)*(1-x^10)*(1-x^11)*(1-x^12)).

%p seq(coeff(series( (1+x^66)/mul((1-x^j), j=1..12)), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Feb 02 2020

%t CoefficientList[Series[(1+x^66)/Product[(1-x^j), {j,12}], {x,0,50}], x] (* _G. C. Greubel_, Feb 02 2020 *)

%o (PARI) Vec( (1+x^66)/prod(j=1,12, 1-x^j) +O('x^50) ) \\ _G. C. Greubel_, Feb 02 2020

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^66)/(&*[1-x^j: j in [1..12]]) )); // _G. C. Greubel_, Feb 02 2020

%o (Sage)

%o def A008631_list(prec):

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

%o     return P( (1+x^66)/product(1-x^j for j in (1..12)) ).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