Triangle, read by rows, T(n, k) = 2*binomial(n, k)*binomial(n+1, k)/(k+1) - (k! - n! + (n-k)!).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =6a(5) =1a(6) =1a(7) =15a(8) =15a(9) =1a(10) =1a(11) =37a(12) =60a(13) =37a(14) =1a(15) =1a(16) =125a(17) =212a(18) =212a(19) =125a(20) =1a(21) =1a(22) =641a(23) =904a(24) =1058a(25) =904a(26) =641a(27) =1a(28) =1a(29) =4375