a(n) = T(2*n+4, n), array T as in A051168 (a count of Lyndon words).

Terms

a(0) =0a(1) =1a(2) =3a(3) =12a(4) =40a(5) =143a(6) =497a(7) =1768a(8) =6288a(9) =22610a(10) =81686a(11) =297160a(12) =1086384a(13) =3991995a(14) =14732005a(15) =54587280a(16) =202995232a(17) =757398510a(18) =2834502346a(19) =10637507400a(20) =40023606896a(21) =150946230006a(22) =570534474698