Number of rooted triangular cacti with 2n+1 nodes (n triangles).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =37a(6) =111a(7) =345a(8) =1105a(9) =3624a(10) =12099a(11) =41000a(12) =140647a(13) =487440a(14) =1704115a(15) =6002600a(16) =21282235a(17) =75890812a(18) =272000538a(19) =979310627a(20) =3540297130a(21) =12845634348a(22) =46764904745a(23) =170767429511a(24) =625314778963