m= 2 blocks=[1, 1] total=        2 half=        1 det_degree=         3
m= 3 blocks=[2, 3, 1] total=        6 half=        3 det_degree=        11
m= 4 blocks=[6, 11, 6, 1] total=       24 half=       12 det_degree=        50
m= 5 blocks=[24, 50, 35, 10, 1] total=      120 half=       60 det_degree=       274
m= 6 blocks=[120, 274, 225, 85, 15, 1] total=      720 half=      360 det_degree=      1764
m= 7 blocks=[720, 1764, 1624, 735, 175, 21, 1] total=     5040 half=     2520 det_degree=     13068
m= 8 blocks=[5040, 13068, 13132, 6769, 1960, 322, 28, 1] total=    40320 half=    20160 det_degree=    109584
m= 9 blocks=[40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1] total=   362880 half=   181440 det_degree=   1026576
m=10 blocks=[362880, 1026576, 1172700, 723680, 269325, 63273, 9450, 870, 45, 1] total=  3628800 half=  1814400 det_degree=  10628640
m=11 blocks=[3628800, 10628640, 12753576, 8409500, 3416930, 902055, 157773, 18150, 1320, 55, 1] total= 39916800 half= 19958400 det_degree= 120543840
m=12 blocks=[39916800, 120543840, 150917976, 105258076, 45995730, 13339535, 2637558, 357423, 32670, 1925, 66, 1] total=479001600 half=239500800 det_degree=1486442880
all exact Stirling, parity, reversed-filtration, and determinant-degree checks passed
