DLMF:26.14.E10 (Q7961)

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DLMF:26.14.E10
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    Statements

    Defining formula
    ∑ k = 0 n - 1 ⟨ n k ⟩ = n ! , superscript subscript 𝑘 0 𝑛 1 Eulerian-number 𝑛 𝑘 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n-1}\genfrac{<}{>}{0.0pt}{}{n}{k}=n!,}}
    0 references
    DLMF id
    DLMF:26.14.E10
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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.m2agdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1hdec
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    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1jdec
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