The triangle in A039754 but with rows truncated at k = n.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =1a(6) =1a(7) =3a(8) =3a(9) =6a(10) =1a(11) =4a(12) =6a(13) =19a(14) =27a(15) =1a(16) =5a(17) =10a(18) =47a(19) =131a(20) =472a(21) =1a(22) =6a(23) =16a(24) =103a(25) =497a(26) =3253a(27) =19735a(28) =1a(29) =7