Triangle read by rows: T(n, k) = [x^k] Sum_{j=0..n} FallingFactorial(n, j)*RisingFactorial(x, j).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =2a(6) =1a(7) =21a(8) =24a(9) =6a(10) =1a(11) =208a(12) =348a(13) =168a(14) =24a(15) =1a(16) =3745a(17) =7520a(18) =4980a(19) =1320a(20) =120a(21) =1a(22) =106116a(23) =237630a(24) =189480a(25) =68760a(26) =11520a(27) =720a(28) =1a(29) =4299589