Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + ((n+1)*(n+2)/2)^2*T(n-2, k-1), read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =38a(5) =1a(6) =1a(7) =139a(8) =139a(9) =1a(10) =1a(11) =365a(12) =8828a(13) =365a(14) =1a(15) =1a(16) =807a(17) =70492a(18) =70492a(19) =807a(20) =1a(21) =1a(22) =1592a(23) =357459a(24) =7062136a(25) =357459a(26) =1592a(27) =1a(28) =1a(29) =2889