a(n) is the number of free n-celled tree-shaped polyominoes.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =11a(5) =27a(6) =83a(7) =255a(8) =847a(9) =2829a(10) =9734a(11) =33724a(12) =118245a(13) =416816a(14) =1478602a(15) =5267171a(16) =18840144a(17) =67611472a(18) =243378415a(19) =878407170a(20) =3178068821a(21) =11523323634a(22) =41865833602a(23) =152382134767