n n! n!*P(n) P(n) 1 1 0 0.000000 2 2 1 0.500000 3 6 2 0.333333 4 24 10 0.416667 5 120 32 0.266667 6 720 232 0.322222 7 5040 992 0.196825 8 40320 10096 0.250397 9 362880 53408 0.147178 10 3628800 727360 0.200441 11 39916800 4569536 0.114477 12 479001600 79501696 0.165974 13 6227020800 578101376 0.092838 14 87178291200 12337163008 0.141516 All numbers are exact except that the final column is rounded to 6 decimals. Arguably the odd-n and even-n subsequences should be separated. Considering even n only... Does the sequence 1, 10, 232, 10096, 727360, 79501696, 12337163008 obey any simple recurrence? I observe that 10-2*3*1 = 4 = 2^2 232-4*5*10 = 32 = 2^5 10096-6*7*232 = 352 = 11*2^5 727360-8*9*10096 = 448 = 7*2^6 79501696-10*11*727360 = -507904 = -31*2^14 12337163008-12*13*79501696 = -65101568 = -254303*2^8 These seem to reveal something interesting happening, but I do not know what it is.