A new q-combination type general triangle sequence based on Stirling first polynomials: here q=5: m=4: 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])].
A156587
A new q-combination type general triangle sequence based on Stirling first polynomials: here q=5: m=4: 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) =5a(5) =1a(6) =1a(7) =30a(8) =30a(9) =1a(10) =1a(11) =210a(12) =1260a(13) =210a(14) =1a(15) =1a(16) =1680a(17) =70560a(18) =70560a(19) =1680a(20) =1a(21) =1a(22) =15120a(23) =5080320a(24) =35562240a(25) =5080320a(26) =15120a(27) =1a(28) =1a(29) =151200
External references
- oeis: A156587