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

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =14a(5) =24a(6) =1a(7) =62a(8) =480a(9) =720a(10) =1a(11) =254a(12) =5544a(13) =30240a(14) =40320a(15) =1a(16) =1022a(17) =54960a(18) =710640a(19) =3024000a(20) =3628800a(21) =1a(22) =4094a(23) =515064a(24) =13654080a(25) =125072640a(26) =439084800a(27) =479001600a(28) =1a(29) =16382