DLMF:26.8.E30 (Q7858)

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DLMF:26.8.E30
No description defined

    Statements

    Defining formula
    ∑ j = k n s ⁡ ( n + 1 , j + 1 ) ⁢ n j - k = s ⁡ ( n , k ) . superscript subscript 𝑗 𝑘 𝑛 Stirling-number-first-kind-S 𝑛 1 𝑗 1 superscript 𝑛 𝑗 𝑘 Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle\sum_{j=k}^{n}s\left(n+1,j+1\right)\,n^{j-k}=s% \left(n,k\right).}}
    0 references
    DLMF id
    DLMF:26.8.E30
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    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.m5aqdec
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    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1idec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1ydec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1addec
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