Triangle read by rows: T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * (3+j)^n.

Terms

a(0) =1a(1) =3a(2) =1a(3) =9a(4) =7a(5) =2a(6) =27a(7) =37a(8) =24a(9) =6a(10) =81a(11) =175a(12) =194a(13) =108a(14) =24a(15) =243a(16) =781a(17) =1320a(18) =1230a(19) =600a(20) =120a(21) =729a(22) =3367a(23) =8162a(24) =11340a(25) =9120a(26) =3960a(27) =720a(28) =2187a(29) =14197