Number of polygonal cacti on n unlabeled nodes with every polygon having an even number of edges.

Terms

a(0) =1a(1) =1a(2) =0a(3) =0a(4) =1a(5) =0a(6) =1a(7) =1a(8) =1a(9) =1a(10) =4a(11) =2a(12) =7a(13) =9a(14) =14a(15) =26a(16) =48a(17) =71a(18) =154a(19) =243a(20) =478a(21) =894a(22) =1631a(23) =3149a(24) =6062a(25) =11295a(26) =22469a(27) =42900a(28) =83528a(29) =164829