A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)*StirlingS1[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])].
A156586
A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)*StirlingS1[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) =4a(5) =1a(6) =1a(7) =20a(8) =20a(9) =1a(10) =1a(11) =120a(12) =600a(13) =120a(14) =1a(15) =1a(16) =840a(17) =25200a(18) =25200a(19) =840a(20) =1a(21) =1a(22) =6720a(23) =1411200a(24) =8467200a(25) =1411200a(26) =6720a(27) =1a(28) =1a(29) =60480
External references
- oeis: A156586