Number of rooted polygonal cacti (Husimi graphs) with n nodes.

Terms

a(0) =0a(1) =1a(2) =0a(3) =1a(4) =1a(5) =3a(6) =5a(7) =13a(8) =27a(9) =67a(10) =157a(11) =390a(12) =963a(13) =2437a(14) =6186a(15) =15908a(16) =41127a(17) =107148a(18) =280569a(19) =738675a(20) =1953054a(21) =5185364a(22) =13816018a(23) =36934431a(24) =99030038a(25) =266254593a(26) =717652816a(27) =1938831589a(28) =5249221790a(29) =14240130827