Roman Factorial

Author

Eric W. Weisstein
April 21, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/RomanFactorial.nb.

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

©2011 Wolfram Research, Inc. except for portions noted otherwise

Code

RomanFactorial[n_]:=Piecewise[{{((((-1))^(-n-1))/((-n-1)!)),n<0}},n!]
FloorCeiling[n_]:=n-(n-1)KroneckerDelta[n]

Values

l=Table[{n,RomanFactorial[n]},{n,-10,10}]

ListLogPlot[l,AxesOrigin->0]

Recurrences

RomanFactorial(n)==FloorCeiling(n) RomanFactorial(n-1)

FullSimplify[RomanFactorial[n]-FloorCeiling[n]RomanFactorial[n-1],n∈Integers]

((RomanFactorial(n))/(RomanFactorial(n-k)))==(∏_(i=0)^(k-1))FloorCeiling(n-i)

FullSimplify[((RomanFactorial[n])/(RomanFactorial[n-k]))-Product[FloorCeiling[n-i],{i,0,k-1}],(n|k)∈Integers]