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) =10a(6) =1a(7) =6a(8) =24a(9) =66a(10) =1a(11) =8a(12) =42a(13) =172a(14) =498a(15) =1a(16) =10a(17) =64a(18) =326a(19) =1360a(20) =4066a(21) =1a(22) =12a(23) =90a(24) =536a(25) =2706a(26) =11444a(27) =34970a(28) =1a(29) =14