Triangle read by rows: T(n, k) = binomial(n, k)/Beta(n+1, n-k+1) + binomial(n, n-k)/Beta(n+1, k+1).

Terms

a(0) =2a(1) =8a(2) =8a(3) =33a(4) =48a(5) =33a(6) =144a(7) =240a(8) =240a(9) =144a(10) =635a(11) =1240a(12) =1260a(13) =1240a(14) =635a(15) =2778a(16) =6510a(17) =6720a(18) =6720a(19) =6510a(20) =2778a(21) =12019a(22) =33600a(23) =38430a(24) =33600a(25) =38430a(26) =33600a(27) =12019a(28) =51488a(29) =168672