Triangle: q=3; m=2; t(n,k)=If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

A156594

Triangle: q=3; m=2; t(n,k)=If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

Terms

    a(0) =1a(1) =1a(2) =1a(3) =1a(4) =-3a(5) =1a(6) =1a(7) =6a(8) =6a(9) =1a(10) =1a(11) =-3a(12) =6a(13) =-3a(14) =1a(15) =1a(16) =-21a(17) =-21a(18) =-21a(19) =-21a(20) =1a(21) =1a(22) =24a(23) =168a(24) =-84a(25) =168a(26) =24a(27) =1a(28) =1a(29) =195

External references