Triangle giving T(n,m) = number of necklaces of two colors with 2n beads of which m=1..n are black.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =4a(6) =1a(7) =4a(8) =7a(9) =10a(10) =1a(11) =5a(12) =12a(13) =22a(14) =26a(15) =1a(16) =6a(17) =19a(18) =43a(19) =66a(20) =80a(21) =1a(22) =7a(23) =26a(24) =73a(25) =143a(26) =217a(27) =246a(28) =1a(29) =8