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 A266775 Molien series for invariants of finite Coxeter group D_12 (bisected). 10
 1, 1, 2, 3, 5, 7, 12, 16, 24, 33, 47, 63, 88, 115, 155, 202, 266, 341, 443, 560, 715, 897, 1129, 1401, 1746, 2146, 2645, 3228, 3941, 4771, 5781, 6948, 8353, 9979, 11913, 14144, 16785, 19814, 23374, 27454, 32211, 37645, 43954, 51130, 59417, 68827, 79631, 91863, 105857, 121645 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. REFERENCES J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA 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. G.f.: 1/( (1-t^6)*Product_{j=1..11} (1-t^j) ). - G. C. Greubel, Feb 01 2020 MAPLE 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 MATHEMATICA CoefficientList[Series[1/((1-t^6)*Product[1-t^j, {j, 11}]), {t, 0, 50}], t] (* G. C. Greubel, Jan 31 2020 *) PROG (PARI) Vec( 1/( (1-x^6)*prod(j=1, 11, 1-x^j) ) + O('x^50)) \\ G. C. Greubel, Jan 31 2020 (MAGMA) R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^6)*(&*[1-x^j: j in [1..11]])) )); // G. C. Greubel, Jan 31 2020 (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 CROSSREFS Molien series for finite Coxeter groups D_3 through D_12 are A266755, A266769, A266768, A003402, and A266770-A266775. Sequence in context: A078912 A105930 A122622 * A024790 A308271 A275592 Adjacent sequences:  A266772 A266773 A266774 * A266776 A266777 A266778 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 11 2016 STATUS approved

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Last modified September 22 20:23 EDT 2020. Contains 337291 sequences. (Running on oeis4.)