Number of noncrossing bridgeless cacti with n nodes.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =1a(5) =6a(6) =13a(7) =57a(8) =169a(9) =673a(10) =2301a(11) =8933a(12) =32747a(13) =127063a(14) =483484a(15) =1889957a(16) =7352241a(17) =29003446a(18) =114481435a(19) =455542880a(20) =1816976042a(21) =7285391071a(22) =29291855748a(23) =118218771203a(24) =478372112363