DLMF:26.7.E4 (Q7820)

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DLMF:26.7.E4
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    Defining formula
    B ⁡ ( n ) = e - 1 ⁢ ∑ k = 1 ∞ k n k ! = 1 + ⌊ e - 1 ⁢ ∑ k = 1 2 ⁢ n k n k ! ⌋ . Bell-number 𝑛 1 superscript subscript 𝑘 1 superscript 𝑘 𝑛 𝑘 1 1 superscript subscript 𝑘 1 2 𝑛 superscript 𝑘 𝑛 𝑘 {\displaystyle{\displaystyle B\left(n\right)={\mathrm{e}^{-1}}\sum_{k=1}^{% \infty}\frac{k^{n}}{k!}=1+\left\lfloor{\mathrm{e}^{-1}}\sum_{k=1}^{2n}\frac{k^% {n}}{k!}\right\rfloor.}}
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    DLMF id
    DLMF:26.7.E4
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