OFFSET
5,2
COMMENTS
Two permutation groups are combinatorially equivalent iff they have the same cycle index. Order of partition is lcm of its parts.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,2,-1,-1,0,1,1,-1).
FORMULA
G.f.: x^5*(1+x-x^6)/((x-1)*(x^2-1)*(x^3-1)*(x^6-1)). More generally, g.f. for number of partitions of order d is Sum_{i divides d} mu(d/i)*1/Product_{j divides i} (1-x^j).
MATHEMATICA
LinearRecurrence[{1, 1, 0, -1, -1, 2, -1, -1, 0, 1, 1, -1}, {1, 2, 3, 5, 7, 9, 12, 16, 19, 24, 29, 34}, 60] (* Harvey P. Dale, May 23 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 28 2002
STATUS
approved