A new general triangle sequence based on the Eulerian form in three parts:m=2; 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)].
A157178
A new general triangle sequence based on the Eulerian form in three parts:m=2; 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) =8a(5) =1a(6) =1a(7) =21a(8) =21a(9) =1a(10) =1a(11) =46a(12) =142a(13) =46a(14) =1a(15) =1a(16) =95a(17) =644a(18) =644a(19) =95a(20) =1a(21) =1a(22) =192a(23) =2439a(24) =5416a(25) =2439a(26) =192a(27) =1a(28) =1a(29) =385
External references
- oeis: A157178