A075534 Number of increasing rooted trees where each node at height h has 0 or h+1 children.

1, 1, 0, 1, 0, 0, 5, 0, 0, 35, 189, 0, 0, 10395, 18018, 77616, 0, 5360355, 15338862, 72648576, 108636528, 4737022290, 47846771280, 84845128368, 833082788538, 6459731648370, 163728321649200, 767835548449200, 3922621945211970