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A008631 Molien series for alternating group Alt_8 (or A_8). 3
1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 230, 288, 352, 434, 525, 638, 764, 919, 1090, 1297, 1527, 1802, 2105, 2464, 2860, 3324, 3835, 4428, 5081, 5834, 6659, 7604, 8640, 9819, 11107, 12566, 14158, 15951, 17904, 20093, 22474, 25133 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,-2,-1,-1,-1,1,1,2,3,0,-1,-1,-4,-1,-1,0,3,2,1,1,-1,-1,-1,-2,1,0,1,1,-1).

FORMULA

G.f.: (1+x^28)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)).

MAPLE

seq(coeff(series( (1+x^28)/mul((1-x^j), j=1..8)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Feb 02 2020

MATHEMATICA

CoefficientList[Series[(1+x^28)/Product[(1-x^j), {j, 1, 8}], {x, 0, 50}], x] (* G. C. Greubel, Feb 02 2020 *)

PROG

(PARI) Vec( (1+x^28)/prod(j=1, 8, 1-x^j) +O('x^50) ) \\ G. C. Greubel, Feb 02 2020

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^28)/(&*[1-x^j: j in [1..8]]) )); // G. C. Greubel, Feb 02 2020

(Sage)

def A008631_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( (1+x^28)/product(1-x^j for j in (1..8)) ).list()

A008631_list(70) # G. C. Greubel, Feb 02 2020

CROSSREFS

Different from A008637.

Sequence in context: A218508 A026814 A008637 * A238866 A035978 A319475

Adjacent sequences:  A008628 A008629 A008630 * A008632 A008633 A008634

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 3 22:43 EDT 2020. Contains 335419 sequences. (Running on oeis4.)