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%I #22 Sep 08 2022 08:46:15
%S 1,1,2,3,5,7,12,16,24,33,47,63,88,115,155,202,266,341,443,560,715,897,
%T 1129,1401,1746,2146,2645,3228,3941,4771,5781,6948,8353,9979,11913,
%U 14144,16785,19814,23374,27454,32211,37645,43954,51130,59417,68827,79631,91863,105857,121645
%N Molien series for invariants of finite Coxeter group D_12 (bisected).
%C The Molien series for the finite Coxeter group of type D_k (k >= 3) has g.f. = 1/Product_i (1-x^(1+m_i)) where the m_i are [1,3,5,...,2k-3,k-1]. If k is even only even powers of x appear, and we bisect the sequence.
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
%H G. C. Greubel, <a href="/A266775/b266775.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%F G.f.: 1/((1-t^2)*(1-t^4)*(1-t^6)*(1-t^8)*(1-t^10)*(1-t^12)^2*(1-t^14)*(1-t^16)*(1-t^18)*(1-t^20)*(1-t^22)), bisected.
%F G.f.: 1/( (1-t^6)*Product_{j=1..11} (1-t^j) ). - _G. C. Greubel_, Feb 01 2020
%p S:=series(1/((1-x^6)*mul(1-x^j, j=1..11)), x, 55): seq(coeff(S, x, j), j=0..50); # _G. C. Greubel_, Jan 31 2020
%t CoefficientList[Series[1/((1-t^6)*Product[1-t^j, {j,11}]), {t,0,50}], t] (* _G. C. Greubel_, Jan 31 2020 *)
%o (PARI) Vec( 1/( (1-x^6)*prod(j=1,11, 1-x^j) ) + O('x^50)) \\ _G. C. Greubel_, Jan 31 2020
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^6)*(&*[1-x^j: j in [1..11]])) )); // _G. C. Greubel_, Jan 31 2020
%o (Sage) [( 1/((1-x^6)*product(1-x^j for j in (1..11))) ).series(x, n+1).list()[n] for n in (0..50)] # _G. C. Greubel_, Jan 31 2020
%Y Molien series for finite Coxeter groups D_3 through D_12 are A266755, A266769, A266768, A003402, and A266770-A266775.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 11 2016
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