Half-factorials (just three examples to show all actual (proven) behaviours) 

 

 

 

p = 3 Here the gamma-values gamma[1], gamma[2], gamma[3], gamma[4], `...` alternate 1, 2, 1, 2, `...` 

 

p = 5 Here the gamma-values gamma[1], gamma[2], gamma[3], gamma[4], `...` are 4, 4, 4, 4, () .. () 

 

p = 7 Here the gamma-values gamma[1], gamma[2], gamma[3], gamma[4], `...` alternate 2, 1, 2, 1, () .. ()