Second-Order Eulerian Triangle

(1)

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

(2)

with initial conditions

(3)

and

(4)

for .

REFERENCES:

Gessel, I. and Stanley, R. P. "Stirling Polynomials." J. Combin. Theory A 24, 24-33, 1978.

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."