Permutation Question

I'm trying to figure out how long it takes for a particular shuffling algorithm to cycle for a particular number of elements. The algorithm is to count from 1 to M, moving the character at position M mod N (N:=number of elements) to the end, and moving everything down so there's no space. [i.e. (indexed from 1 here) g(1,"ABCDEF")="BCDEFA", then g(2,"BCDEFA")="BDEFAC", then g(3,"BDEFAC")="BDFACE", eventually this will cycle; How long? (30 in this example (That's M).)] I've stumped The On-Line Encyclopedia of Integer Sequences, I want to find f() which generates the following sequence, and I don't want to think about this too hard, and I don't have my Knuth books handy (I think it involves factorials).

What is f()?
f(2) = 2
f(3) = 4
f(4) = 9
f(5) = 20
f(6) = 30
f(7) = 36
f(8) = 28
f(9) = 72
f(10)= 36
f(11)= 280
f(12)= 110
f(13)= 108
f(14)= 182
f(15)= 168
f(16)= 75
f(17)= 1120
f(18)= 306
f(19)= 432
f(20)= 190
f(21)= 140
f(22)= 4410
f(23)= 2772
f(24)= 2530
f(25)= 1440
f(26)= 650
f(27)= 3120
f(28)= 243
f(29)= 812
f(30)= 870
f(31)= 1800
f(32)= 186
f(33)= 1056
f(34)= 10164
f(35)= 1428
f(36)= 2100
f(37)= 35640
f(38)= 1110
f(39)= 14212