Triangle read by rows: T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * (5+j)^n.

Terms

a(0) =1a(1) =5a(2) =1a(3) =25a(4) =11a(5) =2a(6) =125a(7) =91a(8) =36a(9) =6a(10) =625a(11) =671a(12) =434a(13) =156a(14) =24a(15) =3125a(16) =4651a(17) =4380a(18) =2550a(19) =840a(20) =120a(21) =15625a(22) =31031a(23) =39962a(24) =33540a(25) =17760a(26) =5400a(27) =720a(28) =78125a(29) =201811