Each row contains the row before as a subsequence:



                                    0
                 1,                 0
        3,       1,           2,    0
   7,   3,   5,  1,   6,      2,4,  0
15,7,12,3,13,5,9,1,14,6,10,11,2,4,8,0





The same for rows 0...7:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0
                                                                                                                                                                                                                            1,                                                                                                                                                                                                                                                                  0
                                                                                                       3,                                                                                                                   1,                                                                                                                                                                                                    2,                                                            0
                                                   7,                                                  3,                                                                                      5,                           1,                                                                                                 6,                                                                                                 2,                                  4,                        0
                        15,                        7,                                  12,             3,                                      13,                                             5,             9,            1,                                      14,                                                        6,                                                               10,11,                            2,                                  4,             8,         0
           31,          15,               26,      7,               28,                12,    20,      3,               29,                    13,                           22,23,            5,             9,   17,      1,               30,                    14,                                      24,25,            6,               27,                                             10,11,          18,19,            2,                   21,            4,             8,16,      0
    67,    31,    57,   15,    62,        26,43,   7,    64,        28,    51,52,      12,    20,36,   3,    65,        29,        53,54,      13,    59,                    22,23,39,40,      5,    45,      9,   17,33,   1,    66,        30,        55,56,      14,        60,61,                        24,25,41,42,      6,63,            27,            46,47,49,48,50,                  10,11,          18,19,34,35,      2,    58,            21,37,38,      4,    44,      8,16,32,   0
147,67,127,31,138,57,96,15,143,62,116,117,26,43,79,7,144,64,121,122,28,133,51,52,90,91,12,101,20,36,72,3,145,65,123,124,29,134,135,53,54,92,93,13,140,59,105,106,108,107,109,22,23,39,40,75,76,5,129,45,82,83,9,97,17,33,69,1,146,66,125,126,30,136,137,55,56,94,95,14,141,142,60,61,110,111,114,112,113,115,24,25,41,42,77,78,6,63,118,119,120,27,130,131,132,46,47,49,48,50,84,85,87,88,86,89,10,11,98,99,100,18,19,34,35,70,71,2,139,58,102,103,104,21,37,38,73,74,4,128,44,80,81,8,16,32,68,0