The Nørlund polynomial (note that the spelling Nörlund also appears in various publications) is a name given by Carlitz (1960) and Adelberg (1997) to the
polynomial .
These are implemented in the Wolfram Language
as NorlundB[n,
a], and are defined through the exponential
generating function

(1)

(Carlitz 1960).

Sums involving
are given by

(2)

(3)

(Carlitz 1960, Gould 1960).

The Nørlund polynomials are related to the Stirling numbers by

Adelberg, A. "Arithmetic Properties of the Nörlund [sic] Polynomial ."
Oct. 28, 1997. http://citeseer.ist.psu.edu/44033.html.Carlitz,
L. "Note on Nörlund's [sic] Polynomial ." Proc. Amer. Math. Soc.11, 452-455,
1960.Gould, H. W. "Stirling Number Representation Problems."
Proc. Amer. Math. Soc.11, 447-451, 1960.Nörlund,
N. E. [sic]. Vorlesungen über Differenzenrechnung. Berlin: Springer-Verlag,
1924.