A008629 - OEIS

A008629

Molien series for A_6.

1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 111, 137, 165, 202, 240, 289, 342, 405, 474, 558, 647, 753, 869, 1002, 1147, 1316, 1496, 1703, 1928, 2180, 2454, 2763, 3093, 3463, 3863, 4304, 4779, 5305, 5866, 6484, 7148, 7870, 8644, 9489, 10387, 11364

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OFFSET

0,3

REFERENCES

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

LINKS

Table of n, a(n) for n=0..50.

Index entries for Molien series

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

FORMULA

G.f.: (1+x^15)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)).

a(n) ~ 1/43200*n^5 + 1/2880*n^4 + 17/8640*n^3. - Ralf Stephan, Apr 29 2014

G.f.: (1-x^3-x+x^2+x^4)*(x^8+x^7-x^5-x^4-x^3+x+1) / ( (x^2+1) *(1+x^3+x+x^2+x^4) *(1+x)^2 *(1+x+x^2)^2 *(x-1)^6 ). - R. J. Mathar, Dec 18 2014

MATHEMATICA

LinearRecurrence[{1, 1, 1, -1, -2, -1, -1, 2, 2, 2, -1, -1, -2, -1, 1, 1, 1, -1}, {1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 111, 137, 165}, 51] (* Ray Chandler, Jul 15 2015 *)

PROG

(Sage)

ring = PowerSeriesRing(ZZ, 'x', default_prec=50)

ms = AlternatingGroup(6).molien_series()

list(ring(ms))

# Ralf Stephan, Apr 29 2014

CROSSREFS

Sequence in context: A026812 A001402 A377077 * A347572 A363068 A238864

Adjacent sequences: A008626 A008627 A008628 * A008630 A008631 A008632

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved