DLMF:26.8.E26 (Q7854)

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DLMF:26.8.E26
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    Statements

    Defining formula
    S ⁡ ( n + k + 1 , k ) = ∑ j = 0 k j ⁢ S ⁡ ( n + j , j ) . Stirling-number-second-kind-S 𝑛 𝑘 1 𝑘 superscript subscript 𝑗 0 𝑘 𝑗 Stirling-number-second-kind-S 𝑛 𝑗 𝑗 {\displaystyle{\displaystyle S\left(n+k+1,k\right)=\sum_{j=0}^{k}jS\left(n+j,j% \right).}}
    0 references
    DLMF id
    DLMF:26.8.E26
    0 references
    Symbols used
    Q12131
    Defining formula
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2andec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1gdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1udec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1zdec
    0 references
     
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