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A266779
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Molien series for invariants of finite Coxeter group A_10.
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3
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1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 20, 23, 32, 38, 50, 59, 77, 90, 115, 135, 168, 197, 243, 283, 344, 401, 481, 558, 665, 767, 906, 1043, 1221, 1401, 1631, 1862, 2155, 2454, 2823, 3203, 3668, 4147, 4727, 5330, 6047, 6798, 7685, 8612, 9700, 10843, 12168, 13566, 15178, 16877, 18825, 20884, 23226, 25707, 28517, 31489, 34842, 38396
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OFFSET
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0,5
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COMMENTS
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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).
Note that this is the root system A_k, not the alternating group Alt_k.
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REFERENCES
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J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 2, 3, 3, 3, 2, 1, 0, -2, -3, -4, -4, -5, -3, -1, 1, 3, 4, 5, 5, 4, 3, 1, -1, -3, -5, -4, -4, -3, -2, 0, 1, 2, 3, 3, 3, 2, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 0, -1).
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FORMULA
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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)).
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MAPLE
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seq(coeff(series(1/mul(1-x^j, j=2..11), x, n+1), x, n), n = 0..70); # G. C. Greubel, Feb 03 2020
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MATHEMATICA
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CoefficientList[Series[1/Product[1-x^j, {j, 2, 11}], {x, 0, 70}], x] (* G. C. Greubel, Feb 03 2020 *)
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PROG
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(PARI) Vec( 1/prod(j=2, 11, 1-x^j) +O('x^70)) \\ G. C. Greubel, Feb 03 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/(&*[1-x^j: j in [2..11]]) )); // G. C. Greubel, Feb 03 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/product(1-x^j for j in (2..11))) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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