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A266780 Molien series for invariants of finite Coxeter group A_11. 2

%I

%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/Prod_{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)).

%t CoefficientList[Series[1/Times@@(1-t^Range[2,12]),{t,0,70}],t] (* _Harvey P. Dale_, Jun 20 2017 *)

%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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Last modified February 19 04:09 EST 2020. Contains 332037 sequences. (Running on oeis4.)