A008634 Molien series for A_11.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 131, 169, 219, 278, 355, 445, 560, 695, 863, 1060, 1303, 1586, 1930, 2331, 2812, 3370, 4035, 4802, 5708, 6751, 7972, 9373, 11004, 12866, 15021, 17475, 20298, 23501, 27169, 31316, 36043, 41373, 47420, 54218, 61903, 70515, 80215, 91058, 103226, 116792, 131970, 148848

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

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

Crossrefs

Differs from A008640 at 55th term.

Programs

Maple

gf:= (1+x^55)/(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)/(1-x^10)/(1-x^11):
seq(coeff(series(gf, x, n+1), x, n), n=0..70);

Mathematica

CoefficientList[Series[(1+x^55)/Times@@(1-x^Range[11]),{x,0,60}],x] (* Harvey P. Dale, Jul 27 2024 *)

Formula

G.f.: (1+x^55)/((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)*(1-x^10)*(1-x^11)).

Extensions

Corrected by Harvey P. Dale, Jul 21 2024

a(55) restored by Sean A. Irvine, Jul 27 2024