DLMF:26.8.E29 (Q7857)

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DLMF:26.8.E29
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    Statements

    Defining formula
    ∑ k = 1 n ( - 1 ) n - k ⁢ s ⁡ ( n , k ) = n ! , superscript subscript 𝑘 1 𝑛 superscript 1 𝑛 𝑘 Stirling-number-first-kind-S 𝑛 𝑘 𝑛 {\displaystyle{\displaystyle\sum_{k=1}^{n}(-1)^{n-k}s\left(n,k\right)=n!,}}
    0 references
    DLMF id
    DLMF:26.8.E29
    0 references
    Symbols used
    Q12132
    Defining formula
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5apdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ahdec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1xdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1acdec
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