DLMF:26.14.E6 (Q7957)

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DLMF:26.14.E6
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    Statements

    Defining formula
    ⟨ n k ⟩ = ∑ j = 0 k ( - 1 ) j ⁢ ( n + 1 j ) ⁢ ( k + 1 - j ) n , Eulerian-number 𝑛 𝑘 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑛 1 𝑗 superscript 𝑘 1 𝑗 𝑛 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{n}{k}=\sum_{j=0}^{k}(-1)^{% j}\genfrac{(}{)}{0.0pt}{}{n+1}{j}(k+1-j)^{n},}}
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    DLMF id
    DLMF:26.14.E6
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    constraint
    n ≥ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
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    Symbols used
    Q12217
    Defining formula
    ⟨ n k ⟩ Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    xml-id
    C26.S14.SS1.p3.m2acdec
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