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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =8a(5) =1a(6) =1a(7) =19a(8) =19a(9) =1a(10) =1a(11) =35a(12) =158a(13) =35a(14) =1a(15) =1a(16) =57a(17) =592a(18) =592a(19) =57a(20) =1a(21) =1a(22) =86a(23) =1629a(24) =5608a(25) =1629a(26) =86a(27) =1a(28) =1a(29) =123