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A266780 Molien series for invariants of finite Coxeter group A_11. 2
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 23, 33, 39, 52, 61, 81, 94, 122, 143, 180, 211, 264, 306, 377, 440, 533, 619, 746, 861, 1028, 1186, 1401, 1612, 1895, 2168, 2532, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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).

Note that this is the root system A_k not the alternating group Alt_k.

REFERENCES

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.

LINKS

Ray Chandler, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, 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).

Index entries for Molien series

FORMULA

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)).

MATHEMATICA

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

CROSSREFS

Molien series for finite Coxeter groups A_1 through A_12 are A059841, A103221, A266755, A008667, A037145, A001996, and A266776-A266781.

Sequence in context: A266779 A035949 A240014 * A266781 A035955 A240015

Adjacent sequences:  A266777 A266778 A266779 * A266781 A266782 A266783

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 11 2016

STATUS

approved

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Last modified January 21 11:16 EST 2020. Contains 331105 sequences. (Running on oeis4.)