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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^36)/(&*[1-x^j: j in [1..9]]) )); // G. C. Greubel, Feb 02 2020

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 *)

PARI

Vec( (1+x^36)/prod(j=1,9, 1-x^j) +O('x^50) ) \\ G. C. Greubel, Feb 02 2020

Sage

def A008631_list(prec):
    P. = 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

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)).

Extensions

More terms from Sean A. Irvine, Apr 01 2018