DLMF:26.7.E4 (Q7820)

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DLMF:26.7.E4
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    Statements

    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.}}
    0 references
    DLMF id
    DLMF:26.7.E4
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    Symbols used
    Q12184
    Defining formula
    B ⁡ ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    xml-id
    C26.S7.SS1.m1acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1bdec
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    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1bdec
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