Triangle, read by rows, T(n, k) = Sum_{j=0..k} (n+k)!/((n-j)!*(k-j)!*j!).

Terms

a(0) =1a(1) =1a(2) =4a(3) =1a(4) =9a(5) =42a(6) =1a(7) =16a(8) =130a(9) =680a(10) =1a(11) =25a(12) =315a(13) =2555a(14) =14630a(15) =1a(16) =36a(17) =651a(18) =7616a(19) =63126a(20) =389592a(21) =1a(22) =49a(23) =1204a(24) =19236a(25) =219450a(26) =1871562a(27) =12314148a(28) =1a(29) =64