A008631 Molien series for alternating group Alt_8 (or A_8).

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

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 *)
LinearRecurrence[{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}, {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}, 70] (* Harvey P. Dale, May 12 2022 *)

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: A340719 A026814 A008637 * A347574 A238866 A035978

Adjacent sequences: A008628 A008629 A008630 * A008632 A008633 A008634

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved