A375303 a(n) is the rank of row n of A130517 in a lexicographic permutation of [1, ..., n].
0, 1, 4, 20, 108, 678, 4848, 39264, 355920, 3575640, 39454560, 474501600, 6178566240, 86606881200, 1300352981760, 20821540239360, 354184575816960, 6378546460970880, 121243261343500800, 2425719783585369600, 50955334461183398400, 1121303792572973856000, 25795667534014525593600
Offset: 1