Triangle T(n,m)=m*n*binomial(m+n,m)^2/(2*(m+n)) read by rows.

Terms

a(0) =1a(1) =3a(2) =18a(3) =6a(4) =60a(5) =300a(6) =10a(7) =150a(8) =1050a(9) =4900a(10) =15a(11) =315a(12) =2940a(13) =17640a(14) =79380a(15) =21a(16) =588a(17) =7056a(18) =52920a(19) =291060a(20) =1280664a(21) =28a(22) =1008a(23) =15120a(24) =138600a(25) =914760a(26) =4756752a(27) =20612592a(28) =36a(29) =1620