Triangle read by rows: T(n,k) = Sum_{j=0..2k} (-1)^j * binomial(2k,j) * (2+k-j)^(2n).

Terms

a(0) =1a(1) =4a(2) =2a(3) =16a(4) =50a(5) =24a(6) =64a(7) =602a(8) =1560a(9) =720a(10) =256a(11) =6050a(12) =40824a(13) =90720a(14) =40320a(15) =1024a(16) =57002a(17) =818520a(18) =4339440a(19) =8467200a(20) =3628800a(21) =4096a(22) =523250a(23) =14676024a(24) =151367040a(25) =663949440a(26) =1157587200a(27) =479001600a(28) =16384a(29) =4750202