Number of unlabeled 3-gonal cacti having n triangles.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =7a(5) =19a(6) =86a(7) =372a(8) =1825a(9) =9143a(10) =47801a(11) =254990a(12) =1391302a(13) =7713642a(14) =43401974a(15) =247216934a(16) =1423531255a(17) =8275108733a(18) =48511773461a(19) =286542497274