A032306 Number of rooted trees with leaves of 2 colors where any 2 subtrees extending from the same node have a different number of nodes.

2, 2, 2, 6, 10, 26, 66, 174, 442, 1202, 3298, 9166, 25674, 72810, 206826, 595150, 1712634, 4978458, 14494130, 42502030, 124660402, 368221002, 1087321354, 3229266742, 9591013738, 28624735962, 85404444970