DLMF:26.8.E33 (Q7861)

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DLMF:26.8.E33
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    Defining formula
    S ⁡ ( n , n - k ) = ∑ j = 0 k ( - 1 ) j ⁢ ( n - 1 + j k + j ) ⁢ ( n + k k - j ) ⁢ s ⁡ ( k + j , j ) , Stirling-number-second-kind-S 𝑛 𝑛 𝑘 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑛 1 𝑗 𝑘 𝑗 binomial 𝑛 𝑘 𝑘 𝑗 Stirling-number-first-kind-S 𝑘 𝑗 𝑗 {\displaystyle{\displaystyle S\left(n,n-k\right)=\sum_{j=0}^{k}(-1)^{j}% \genfrac{(}{)}{0.0pt}{}{n-1+j}{k+j}\genfrac{(}{)}{0.0pt}{}{n+k}{k-j}\*s\left(k% +j,j\right),}}
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    DLMF id
    DLMF:26.8.E33
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