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%I #15 Feb 23 2022 23:05:55
%S 1,0,1,1,2,2,4,4,7,8,12,14,21,23,33,39,52,61,81,94,122,143,180,211,
%T 264,306,377,440,533,619,746,861,1028,1186,1401,1612,1895,2168,2532,
%U 2894,3356,3822,4414,5008,5755,6516,7448,8410,9580,10780,12232,13737,15524,17388,19592,21885,24580,27400,30674,34117,38097,42269,47074,52133
%N Molien series for invariants of finite Coxeter group A_11.
%C The Molien series for the finite Coxeter group of type A_k (k >= 1) has g.f. = 1/Product_{i=2..k+1} (1 - x^i).
%C Note that this is the root system A_k, not the alternating group Alt_k.
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
%H Ray Chandler, <a href="/A266780/b266780.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_77">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, 0, -1, -1, 1, 2, 3, 3, 3, 2, 1, -1, -2, -3, -3, -5, -5, -4, -2, 0, 2, 4, 5, 6, 6, 5, 3, 2, -2, -3, -5, -6, -6, -5, -4, -2, 0, 2, 4, 5, 5, 3, 3, 2, 1, -1, -2, -3, -3, -3, -2, -1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, -1, -1, -1, 0, 1).
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%F G.f.: 1/((1-t^2)*(1-t^3)*(1-t^4)*(1-t^5)*(1-t^6)*(1-t^7)*(1-t^8)*(1-t^9)*(1-t^10)*(1-t^11)*(1-t^12)).
%p S:=series(1/mul(1-x^j, j=2..12)), x, 75):
%p seq(coeff(S, x, j), j=0..70); # _G. C. Greubel_, Feb 04 2020
%t CoefficientList[Series[1/Times@@(1-t^Range[2,12]),{t,0,70}],t] (* _Harvey P. Dale_, Jun 20 2017 *)
%o (PARI) Vec( 1/prod(j=2,12, 1-x^j) +O('x^70) ) \\ _G. C. Greubel_, Feb 04 2020
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/(&*[1-x^j: j in [2..12]]) )); // _G. C. Greubel_, Feb 04 2020
%o (Sage)
%o def A266780_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/prod(1-x^j for j in (2..12)) ).list()
%o A266780_list(70) # _G. C. Greubel_, Feb 04 2020
%Y Molien series for finite Coxeter groups A_1 through A_12 are A059841, A103221, A266755, A008667, A037145, A001996, and A266776-A266781.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Jan 11 2016
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