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

Terms

a(0) =1a(1) =3a(2) =1a(3) =8a(4) =7a(5) =1a(6) =21a(7) =34a(8) =12a(9) =1a(10) =55a(11) =141a(12) =89a(13) =18a(14) =1a(15) =144a(16) =534a(17) =522a(18) =186a(19) =25a(20) =1a(21) =377a(22) =1905a(23) =2651a(24) =1445a(25) =340a(26) =33a(27) =1a(28) =987a(29) =6512