Triangle read by rows of numbers of paths in a lattice satisfying certain conditions.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =4a(5) =7a(6) =1a(7) =6a(8) =18a(9) =30a(10) =1a(11) =8a(12) =33a(13) =88a(14) =143a(15) =1a(16) =10a(17) =52a(18) =182a(19) =455a(20) =728a(21) =1a(22) =12a(23) =75a(24) =320a(25) =1020a(26) =2448a(27) =3876a(28) =1a(29) =14