A new general triangle sequence based on the Eulerian form in three parts:m=1; t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) + (m*k + 1)*t0(n - 1 + 1, k) + m*k*(n - k)*t0(n - 2 + 1, k - 1)].

A157177

A new general triangle sequence based on the Eulerian form in three parts:m=1; t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) + (m*k + 1)*t0(n - 1 + 1, k) + m*k*(n - k)*t0(n - 2 + 1, k - 1)].

Terms

    a(0) =1a(1) =1a(2) =1a(3) =1a(4) =5a(5) =1a(6) =1a(7) =13a(8) =13a(9) =1a(10) =1a(11) =29a(12) =82a(13) =29a(14) =1a(15) =1a(16) =61a(17) =368a(18) =368a(19) =61a(20) =1a(21) =1a(22) =125a(23) =1399a(24) =3010a(25) =1399a(26) =125a(27) =1a(28) =1a(29) =253

External references