A093458 Partial products of A073846.

1, 2, 8, 24, 144, 720, 5760, 40320, 362880, 3991680, 39916800, 518918400, 6227020800, 105859353600, 1482030950400, 28158588057600, 422378820864000, 9714712879872000, 155435406077952000, 4507626776260608000

Offset: 0

Author

Amarnath Murthy, Apr 03 2004

Keywords

• less
• nonn

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]

Crossrefs

Cf. A073846, A093459.

Programs

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 *)

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.

Extensions

More terms from David Wasserman, Sep 28 2006