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A093458 Mixed factorials. Define MF(n) as the product prime(1)*composite(1)*(prime(2)*composite(2)...prime(n/2)*composite(n/2) if n is even else MF(n) as the product prime(1)*composite(1)*(prime(2)*composite(2)*...*prime((n+1)/2). a(0)= 1. 1
1, 2, 8, 24, 144, 720, 5760, 40320, 362880, 3991680, 39916800, 518918400, 6227020800, 105859353600, 1482030950400, 28158588057600, 422378820864000, 9714712879872000, 155435406077952000, 4507626776260608000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial product of A073846.

a(n-1) 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]

LINKS

Table of n, a(n) for n=1..20.

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

Cf. A073846, A093459.

Sequence in context: A087982 A176475 A145238 * A242456 A088994 A214849

Adjacent sequences:  A093455 A093456 A093457 * A093459 A093460 A093461

KEYWORD

less,nonn

AUTHOR

Amarnath Murthy, Apr 03 2004

EXTENSIONS

More terms from David Wasserman, Sep 28 2006

STATUS

approved

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Last modified December 9 16:22 EST 2016. Contains 278985 sequences.