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Second-Order Eulerian Triangle

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(1)

The second-order Eulerian triangle (OEIS A008517) is the number triangle defined by the recurrence equation

T(n,k)=(k+1)T(n-1,k)+(2n-k-1)T(n-1,k-1)
(2)

for integer indices n>=2 and 1<=k<n, with initial conditions

T(n,0)=1
(3)

for n>=1 and

T(n,k)=0
(4)

for n>=1 and k>=n.

See also

Euler's Number Triangle, Number Triangle

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References

Gessel, I. and Stanley, R. P. "Stirling Polynomials." J. Combin. Theory A 24, 24-33, 1978. https://doi.org/10.1016/0097-3165(78)90042-0.Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, p. 256, 1994.Munch, O. J. "Om potensproduktsummer." Nordisk Matematisk Tidskrift 7, 5-19, 1959.Sloane, N. J. A. Sequence A008517 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Second-Order Eulerian Triangle

Cite this as:

Weisstein, Eric W. "Second-Order Eulerian Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Second-OrderEulerianTriangle.html

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