Triangle T(n, k) = [x^n] (n + k + x)!/(k + x)! for 0 <= k <= n, read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =1a(6) =6a(7) =26a(8) =12a(9) =1a(10) =24a(11) =154a(12) =119a(13) =22a(14) =1a(15) =120a(16) =1044a(17) =1175a(18) =355a(19) =35a(20) =1a(21) =720a(22) =8028a(23) =12154a(24) =5265a(25) =835a(26) =51a(27) =1a(28) =5040a(29) =69264