Number of noncrossing 2,3 cacti with n nodes.

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =20a(5) =115a(6) =715a(7) =4683a(8) =31824a(9) =222300a(10) =1586310a(11) =11514030a(12) =84742320a(13) =630946446a(14) =4743789260a(15) =35965715780a(16) =274659794160