Completion of a Rational Function Sequence of Carlitz

Details Completion of a Rational Function Sequence of Carlitz Completion of a Rational Function Sequence of Carlitz

2000-06-14

arxiv.org/abs/math/0006106v1

Mathematics

Combinatorics

8 pages

Scientific paper

The exponential generating functions of {n^(n+m)} for arbitrary integer m are expressed as rational functions of the e.g.f. of {n^(n-1)} [the tree function] and then of the e.g.f. of {n^n} [the endofunction function]. The coefficients in these rational functions include 2nd-order Eulerian numbers (a result of L. Carlitz), 2nd-order Stirling numbers, and Stirling numbers of the first kind for negative sets (in the sense of D. Loeb). Several combinatorial identities follow.

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