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%I #25 Dec 17 2015 03:20:59
%S 1,2,6,12,24,48,120,144,240,288,720,1440,2880,4320,5040,5760,8640,
%T 10080,17280,30240,34560,40320,60480,80640,86400,103680,120960,172800,
%U 207360,241920,362880,483840,518400,604800,725760,967680,1036800,1209600
%N Products of distinct factorials.
%C (A075082(n)!)^2 is a member for n>0, for example, (6!)^2=6!*5!*3!. Factorials A000142 and superfactorials A000178 (without their first terms), double-superfactorials A098694 and product-of-next-n-factorials A074319 are all subsequences. Products-of-factorials A001013 is a supersequence. - _Jonathan Sondow_, Dec 18 2004
%C A000197(n)^2 is a member for n > 2, as ((n!)!)^2 = (n!)!*n!*(n!-1)!. - _Jonathan Sondow_, Dec 21 2004
%C Erdős & Graham show that there are exp((1+o(1))n log log n / log n) members of this sequence using no factorials above n.
%H Charles R Greathouse IV, <a href="/A058295/b058295.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Erdős and Ron L. Graham, <a href="http://www.math.ucsd.edu/~ronspubs/76_12_factorial_products.pdf">On products of factorials</a>, Bull. Inst. Math. Acad. Sinica 4:2 (1976), pp. 337-355.
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e 288 is included because 288 = 2! * 3! * 4!.
%t k=10; m=1; With[{p=With[{s=Subsets[Table[n!, {n, 2, k}]]}, Sort[Table[Apply[Times, s[[n]]], {n, Length[s]}]]]}, While[p[[m]]<(k+1)!, m++ ]; Union[Take[p, m-1]]] (* _Jonathan Sondow_ *)
%o (PARI) list(lim)=my(v=List([1]),n=1,t=1);while((t=n++!)<=lim,for(i=1,#v,if(v[i]*t<=lim,listput(v,v[i]*t))));vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Mar 26 2012
%Y Cf. A075082, A000142, A000178, A098694, A074319, A001013, A000197.
%K nonn
%O 1,2
%A _Leroy Quet_, Dec 07 2000
%E Corrected by _Jonathan Sondow_, Dec 18 2004
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