Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 2, n-k) for n>=k>=0.

Terms

a(0) =1a(1) =3a(2) =1a(3) =15a(4) =5a(5) =1a(6) =220a(7) =55a(8) =8a(9) =1a(10) =7315a(11) =1330a(12) =153a(13) =12a(14) =1a(15) =435897a(16) =58905a(17) =5456a(18) =351a(19) =17a(20) =1a(21) =40475358a(22) =4187106a(23) =316251a(24) =17296a(25) =703a(26) =23a(27) =1a(28) =5373200880a(29) =437353560