DLMF:26.8.E23 (Q7851)

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DLMF:26.8.E23
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    Statements

    Defining formula
    ( k h ) ⁢ S ⁡ ( n , k ) = ∑ j = k - h n - h ( n j ) ⁢ S ⁡ ( n - j , h ) ⁢ S ⁡ ( j , k - h ) , binomial 𝑘 ℎ Stirling-number-second-kind-S 𝑛 𝑘 superscript subscript 𝑗 𝑘 ℎ 𝑛 ℎ binomial 𝑛 𝑗 Stirling-number-second-kind-S 𝑛 𝑗 ℎ Stirling-number-second-kind-S 𝑗 𝑘 ℎ {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{k}{h}S\left(n,k\right)=% \sum_{j=k-h}^{n-h}\genfrac{(}{)}{0.0pt}{}{n}{j}S\left(n-j,h\right)S\left(j,k-h% \right),}}
    0 references
    DLMF id
    DLMF:26.8.E23
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    constraint
    n ≥ k ≥ h 𝑛 𝑘 ℎ {\displaystyle{\displaystyle n\geq k\geq h}}
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    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.m2akdec
    0 references
     
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