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

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =4a(5) =2a(6) =3a(7) =11a(8) =13a(9) =5a(10) =4a(11) =25a(12) =51a(13) =43a(14) =13a(15) =5a(16) =49a(17) =149a(18) =203a(19) =130a(20) =32a(21) =6a(22) =86a(23) =364a(24) =716a(25) =734a(26) =382a(27) =80a(28) =7a(29) =139