Eulerian numbers

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1: 26.14 Permutations: Order Notation

… ►The Eulerian number, denoted , is the number of permutations in ${𝔖}_n$ with exactly $k$ descents. … ►

Table 26.14.1: Eulerian numbers .

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$n$	$k$
	…

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26.14.9 $n\ge 1$,

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Symbols:

: Eulerian number, $k$: nonnegative integer and $n$: nonnegative integer

Permalink:

http://dlmf.nist.gov/26.14.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §26.14(iii), §26.14 and Ch.26

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26.14.14

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Symbols:

: Eulerian number and $n$: nonnegative integer

Permalink:

http://dlmf.nist.gov/26.14.E14

Encodings:

pMML, png, TeX

See also:

Annotations for §26.14(iv), §26.14 and Ch.26

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26.14.15 $n\ge 1$,

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Symbols:

: Eulerian number and $n$: nonnegative integer

Permalink:

http://dlmf.nist.gov/26.14.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §26.14(iv), §26.14 and Ch.26

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2: 26.1 Special Notation

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$\left(\genfrac{}{}{0.0pt}{}{m}{n}\right)$	binomial coefficient.
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	Eulerian number.
…

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3: 24.4 Basic Properties

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§24.4(ix) Relations to Other Functions

►For the relation of Bernoulli numbers to the Riemann zeta function see §25.6, and to the Eulerian numbers see (26.14.11).

4: Bibliography C

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$q$-Bernoulli and Eulerian numbers. Trans. Amer. Math. Soc. 76 (2), pp. 332–350.

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External Links:

FullText, MathReview (A. L. Whiteman), ZentralBlatt

Referenced by:

§17.3(iii), §24.16(iii).

Encodings:

BibTeX

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