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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =19a(7) =48a(8) =126a(9) =355a(10) =1037a(11) =3124a(12) =9676a(13) =30604a(14) =98473a(15) =321572a(16) =1063146a(17) =3552563a(18) =11982142a(19) =40746208a(20) =139573646a(21) =481232759a(22) =1669024720a(23) =5819537836a(24) =20390462732a(25) =71762924354a(26) =253601229046a(27) =899586777908