Number of unlabeled asymmetric ternary cacti having n triangles.

Terms

a(0) =1a(1) =1a(2) =0a(3) =3a(4) =10a(5) =54a(6) =222a(7) =1107a(8) =5346a(9) =27399a(10) =142770a(11) =764967a(12) =4170672a(13) =23140813a(14) =130189302a(15) =741650172a(16) =4270501218a(17) =24825326196a(18) =145534796520a(19) =859627488963