Triangle T(n, k) = Sum_{m=0..k} Sum_{j=0..m} Multinomial(n-k-m-j, j, m, k), read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =1a(6) =1a(7) =15a(8) =6a(9) =1a(10) =1a(11) =40a(12) =36a(13) =8a(14) =1a(15) =1a(16) =85a(17) =160a(18) =60a(19) =10a(20) =1a(21) =1a(22) =156a(23) =615a(24) =340a(25) =90a(26) =12a(27) =1a(28) =1a(29) =259