%I #20 Jan 10 2024 04:57:48
%S 1,2,8,24,144,720,5760,40320,362880,3991680,39916800,518918400,
%T 6227020800,105859353600,1482030950400,28158588057600,422378820864000,
%U 9714712879872000,155435406077952000,4507626776260608000
%N Partial products of A073846.
%C 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]
%F 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.
%t g[list_]:=Total[list]! / Apply[Times,list] / Apply[Times,Table[Count[list,n]!,{n,1,20}]];
%t f[list_]:=Apply[Plus,Table[Count[list,n],{n,2,20,2}]];
%t Drop[Table[Max[Map[g,Select[Partitions[n],EvenQ[f[#]]&]]],{n,1,20}]]
%t (* _Geoffrey Critzer_, Mar 26 2013 *)
%Y Cf. A073846, A093459.
%K less,nonn
%O 0,2
%A _Amarnath Murthy_, Apr 03 2004
%E More terms from _David Wasserman_, Sep 28 2006
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