OFFSET
0,2
COMMENTS
a(n-2) is the number of elements in the largest conjugacy class of A_n, the alternating group on n letters. Cf. A059171. [Geoffrey Critzer, Mar 26 2013]
FORMULA
a(n) = prime(1) * composite(1) * prime(2) * composite(2) * ... * prime(n/2) * composite(n/2) if n is even else a(n) = prime(1) * composite(1) * prime(2) * composite(2) * ... * prime((n+1)/2). a(0) = 1.
MATHEMATICA
g[list_]:=Total[list]! / Apply[Times, list] / Apply[Times, Table[Count[list, n]!, {n, 1, 20}]];
f[list_]:=Apply[Plus, Table[Count[list, n], {n, 2, 20, 2}]];
Drop[Table[Max[Map[g, Select[Partitions[n], EvenQ[f[#]]&]]], {n, 1, 20}]]
(* Geoffrey Critzer, Mar 26 2013 *)
CROSSREFS
KEYWORD
less,nonn
AUTHOR
Amarnath Murthy, Apr 03 2004
EXTENSIONS
More terms from David Wasserman, Sep 28 2006
STATUS
approved