Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =2a(4) =0a(5) =4a(6) =12a(7) =36a(8) =120a(9) =392a(10) =1288a(11) =4284a(12) =14304a(13) =48024a(14) =162024a(15) =548872a(16) =1866416a(17) =6368464a(18) =21797776a(19) =74822636a(20) =257513344a(21) =888439192a(22) =3072153864a(23) =10645835384a(24) =36964041872a(25) =128584760560a(26) =448087042160