Triangle T(n, k) = binomial(n+1, k)*A142458(n+1, k+1)/(k+1), read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =12a(5) =1a(6) =1a(7) =78a(8) =78a(9) =1a(10) =1a(11) =415a(12) =1820a(13) =415a(14) =1a(15) =1a(16) =2031a(17) =27410a(18) =27410a(19) =2031a(20) =1a(21) =1a(22) =9534a(23) =330225a(24) =959350a(25) =330225a(26) =9534a(27) =1a(28) =1a(29) =43660