Number of unlabeled ternary cacti having n triangles.

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =19a(5) =57a(6) =258a(7) =1110a(8) =5475a(9) =27429a(10) =143379a(11) =764970a(12) =4173906a(13) =23140816a(14) =130205922a(15) =741650802a(16) =4270593219a(17) =24825326199a(18) =145535320383a(19) =859627488966