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%I #13 Jun 13 2012 01:38:43
%S 1,2,6,12,24,120,144,288,720,2880,5040,17280,34560,40320,86400,362880,
%T 2073600,3628800,12441600,24883200,39916800,203212800,435456000,
%U 479001600,6227020800,10450944000,14631321600,62705664000,87178291200
%N Product of consecutive factorials.
%C It appears that only 3628800 and 53094139822080000 have more than one representation. We have 3628800 = 10! = 6! * 7! and 53094139822080000 = 8! * 9! * 10! = 6! * 7! * 8! * 9!. - _T. D. Noe_, Jun 13 2012
%H T. D. Noe, <a href="/A034882/b034882.txt">Table of n, a(n) for n = 1..1000</a>
%t Union[Reap[For[x1=1, x1 <= 14, x1++, x2=x1; a=x1!; While[a < 10^11, Sow[a]; x2 = x2+1; a = a*x2!]]][[2, 1]]] (* _Jean-François Alcover_, Jun 11 2012, after PARI *)
%t nn = 20; t = Range[nn]!; j = 2; While[i = 2; new = 0; While[p = Times @@ Take[t, {i, i + j - 1}]; p < t[[nn]], AppendTo[t, p]; new++; i++]; new > 0, j++]; t = Union[t] (* _T. D. Noe_, Jun 13 2012 *)
%o (PARI) l=listcreate(100)
%o for(x1=1,14,x2=x1;a=x1!;while(a<1e11,listput(l,a);x2=x2+1;a=a*x2!))
%o listsort(l,1);print(l)
%o /* _Michael B. Porter_, Mar 15 2010 */
%K easy,nonn,nice
%O 1,2
%A _Erich Friedman_
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