Factorial Products

Author

Eric W. Weisstein
January 20, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/FactorialProducts.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FactorialProducts.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Products of Factorials

Rest[FoldList[Times,1,Range[6]!]]

All Possible Products

(f[1,n_,ll_]:={#}&/@Select[ll,#≤n&];
f[k_,0,ll_]:={};
f[k_,n_,ll_]/;k>Length[ll]:={};
f[k_,n_,ll_]/;k==Length[ll]:=If[(Times@@ll)≤n,{ll},{}];
f[k_,n_,ll_]:=Join@@((Function[l,Append[l,ll[[#]]]]/@f[k-1,Floor[n/ll[[#]]],ll])&/@Range[Length[ll]-k]))

Union[Flatten[(Times@@@f[#,10^4,Range[10]!])&/@Range[10]]]//Timing