A050339 Number of factorizations with 2 levels of parentheses indexed by prime signatures. A050338(A025487).

1, 1, 4, 4, 10, 16, 30, 54, 22, 75, 74, 176, 102, 206, 267, 535, 399, 518, 950, 526, 1585, 154, 1094, 1446, 1344, 3091, 2252, 4527, 817, 4158, 4879, 3357, 9809, 8811, 12664, 3605, 14653, 3005, 15738, 8429, 10479, 29762, 4777, 16863, 31883, 34631