Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+2, n-k).

Terms

a(0) =1a(1) =3a(2) =1a(3) =10a(4) =4a(5) =1a(6) =56a(7) =21a(8) =5a(9) =1a(10) =495a(11) =165a(12) =36a(13) =6a(14) =1a(15) =6188a(16) =1820a(17) =364a(18) =55a(19) =7a(20) =1a(21) =100947a(22) =26334a(23) =4845a(24) =680a(25) =78a(26) =8a(27) =1a(28) =2035800a(29) =475020