T(n, k) = Sum_{i=0, n} (Sum_{j=0, k} C(i+j,i) * C(n-i+j,n-i) * C(i+k-j,k-j) * C(n-i+k-j,n-i)).

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =8a(5) =3a(6) =4a(7) =20a(8) =20a(9) =4a(10) =5a(11) =40a(12) =76a(13) =40a(14) =5a(15) =6a(16) =70a(17) =216a(18) =216a(19) =70a(20) =6a(21) =7a(22) =112a(23) =511a(24) =832a(25) =511a(26) =112a(27) =7a(28) =8a(29) =168