Triangle, read by rows, T(n,k) = (k+1)*Sum_{i=0..n-k} C(k+2*i,i)*C(n-i-1,n-k-i)/(k+i+1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =1a(6) =5a(7) =8a(8) =5a(9) =1a(10) =14a(11) =22a(12) =18a(13) =7a(14) =1a(15) =42a(16) =64a(17) =59a(18) =32a(19) =9a(20) =1a(21) =132a(22) =196a(23) =190a(24) =124a(25) =50a(26) =11a(27) =1a(28) =429a(29) =625