OFFSET
1,2
COMMENTS
(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
A000197(n)^2 is a member for n > 2, as ((n!)!)^2 = (n!)!*n!*(n!-1)!. - Jonathan Sondow, Dec 21 2004
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.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Paul Erdős and Ron L. Graham, On products of factorials, Bull. Inst. Math. Acad. Sinica 4:2 (1976), pp. 337-355.
EXAMPLE
288 is included because 288 = 2! * 3! * 4!.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 07 2000
EXTENSIONS
Corrected by Jonathan Sondow, Dec 18 2004
STATUS
approved