A034882 Product of consecutive factorials.

1, 2, 6, 12, 24, 120, 144, 288, 720, 2880, 5040, 17280, 34560, 40320, 86400, 362880, 2073600, 3628800, 12441600, 24883200, 39916800, 203212800, 435456000, 479001600, 6227020800, 10450944000, 14631321600, 62705664000, 87178291200

Offset: 1

Author

Erich Friedman

Keywords

• easy
• nonn
• nice

Comments

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Mathematica

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 *)
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 *)

PARI

l=listcreate(100)
for(x1=1,14,x2=x1;a=x1!;while(a<1e11,listput(l,a);x2=x2+1;a=a*x2!))
listsort(l,1);print(l)
/* Michael B. Porter, Mar 15 2010 */