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Completion of a Rational Function Sequence of Carlitz | Leonard M. Smiley
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14 Jun 2000 | Subject: | Combinatorics MSC-class: 05A19 ; 11B73 ; 05A15 | math.CO | Abstract: | 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. | Source: | arXiv, math.CO/0006106 | Services: | Forum | Review | PDF | Favorites |
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