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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
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<x>:=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 A360622
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 11 2016
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)