DLMF:26.8.E21 (Q7849)

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DLMF:26.8.E21
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    Statements

    Defining formula
    s ⁡ ( n + k + 1 , k ) = - ∑ j = 0 k ( n + j ) ⁢ s ⁡ ( n + j , j ) . Stirling-number-first-kind-S 𝑛 𝑘 1 𝑘 superscript subscript 𝑗 0 𝑘 𝑛 𝑗 Stirling-number-first-kind-S 𝑛 𝑗 𝑗 {\displaystyle{\displaystyle s\left(n+k+1,k\right)=-\sum_{j=0}^{k}(n+j)s\left(% n+j,j\right).}}
    0 references
    DLMF id
    DLMF:26.8.E21
    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.m5amdec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1cdec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1pdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1udec
    0 references
     
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