A008628 Molien series for A_5.

1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 38, 49, 60, 75, 91, 111, 132, 159, 187, 222, 258, 302, 348, 403, 461, 528, 599, 681, 767, 866, 969, 1086, 1209, 1347, 1492, 1653, 1822, 2009, 2205, 2421, 2646, 2893, 3151, 3432, 3726, 4044, 4376, 4735, 5109, 5512, 5931

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..51.

Index entries for Molien series

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

Formula

a(n) ~ 1/1440*n^4 + 1/144*n^3. - Ralf Stephan, Apr 29 2014

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

Maple

(1+x^10)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5): seq(coeff(series(%, x, n+1), x, n), n=0..60);

Mathematica

LinearRecurrence[{1, 2, -1, -2, 0, 1, -1, 0, 2, 1, -2, -1, 1}, {1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 38, 49}, 52] (* Ray Chandler, Jul 15 2015 *)

Prog

(Sage)
ring = PowerSeriesRing(ZZ, 'x', default_prec=50)
ms = AlternatingGroup(5).molien_series()
list(ring(ms))
# Ralf Stephan, Apr 29 2014

Crossrefs

Sequence in context: A026811 A001401 A347549 * A363067 A038499 A118199

Adjacent sequences: A008625 A008626 A008627 * A008629 A008630 A008631

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved