Completion of a Rational Function Sequence of Carlitz
组合数学
2016-09-07 v1
摘要
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.
引用
@article{arxiv.math/0006106,
title = {Completion of a Rational Function Sequence of Carlitz},
author = {Leonard M. Smiley},
journal= {arXiv preprint arXiv:math/0006106},
year = {2016}
}
备注
8 pages