Triangle T(n, m) = (n - m + 1)*C(2*n + 1, m)*C(2*n - m + 2, n - m + 1)/(2*n - m + 2).

Terms

a(0) =1a(1) =3a(2) =3a(3) =10a(4) =20a(5) =10a(6) =35a(7) =105a(8) =105a(9) =35a(10) =126a(11) =504a(12) =756a(13) =504a(14) =126a(15) =462a(16) =2310a(17) =4620a(18) =4620a(19) =2310a(20) =462a(21) =1716a(22) =10296a(23) =25740a(24) =34320a(25) =25740a(26) =10296a(27) =1716a(28) =6435a(29) =45045