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a(n) = n!/A102356(n).
3

%I #13 Jan 24 2014 10:00:34

%S 1,1,2,2,4,8,12,24,48,96,288,576,1152,2304,6912,13824,27648,82944,

%T 165888,497664,1327104,2985984,7962624,19906560,59719680,143327232,

%U 358318080,955514880,2866544640,7644119040,17199267840,51597803520,137594142720,412782428160

%N a(n) = n!/A102356(n).

%H Alois P. Heinz, <a href="/A102456/b102456.txt">Table of n, a(n) for n = 0..500</a>

%p b:= proc(n, i) option remember;

%p `if`(n=0, 1, `if` (i<1, 0,

%p max(seq(b(n-i*j, i-1) *n!/i!^j/(n-i*j)!/j!, j=0..n/i))))

%p end:

%p a:= n-> n!/b(n, n):

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Jun 01 2012

%t b[0, _] = 1; b[_, _?NonPositive] = 0; b[n_, i_] := b[n, i] = Max[Table[b[n - i*j, i - 1]*n!/i!^j/(n - i*j)!/j!, {j, 0, n/i}]]; a[n_] := n!/b[n, n]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Jan 24 2014, after _Alois P. Heinz_ *)

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Feb 23 2005