A008632 Molien series for A_9.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 73, 94, 123, 157, 201, 252, 318, 393, 488, 598, 732, 887, 1076, 1291, 1549, 1845, 2194, 2592, 3060, 3589, 4206, 4904, 5708, 6615, 7658, 8825, 10158, 11651, 13343, 15231, 17365, 19735, 22402, 25361, 28670

Offset

0,3

References

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

Links

Sean A. Irvine, 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,-1,2,0,1,3,-1,1,0,-3,0,-2,-1,1,-1,1,2,0,3,0,-1,1,-3,-1,0,-2,1,1,1,2,-1,0,-1,-1,1).

Formula

G.f.: (1+x^36)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)* (1-x^9)).

Maple

seq(coeff(series( (1+x^36)/mul((1-x^j), j=1..9)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Feb 02 2020

Mathematica

CoefficientList[Series[(1+x^36)/Product[(1-x^j), {j, 1, 9}], {x, 0, 50}], x] (* G. C. Greubel, Feb 02 2020 *)

Prog

(PARI) Vec( (1+x^36)/prod(j=1, 9, 1-x^j) +O('x^50) ) \\ G. C. Greubel, Feb 02 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^36)/(&*[1-x^j: j in [1..9]]) )); // G. C. Greubel, Feb 02 2020
(Sage)
def A008631_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^36)/product(1-x^j for j in (1..9)) ).list()
A008631_list(70) # G. C. Greubel, Feb 02 2020

Crossrefs

Sequence in context: A026815 A341913 A008638 * A347575 A238867 A035988

Adjacent sequences: A008629 A008630 A008631 * A008633 A008634 A008635

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 01 2018

Status

approved