DLMF:26.13.E4 (Q7949)

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English
DLMF:26.13.E4
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    Statements

    Defining formula
    d ⁢ ( n ) = n ! ⁢ ∑ j = 0 n ( - 1 ) j ⁢ 1 j ! = ⌊ n ! + e - 2 e ⌋ . 𝑑 𝑛 𝑛 superscript subscript 𝑗 0 𝑛 superscript 1 𝑗 1 𝑗 𝑛 2 {\displaystyle{\displaystyle d(n)=n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}=\left% \lfloor\frac{n!+\mathrm{e}-2}{\mathrm{e}}\right\rfloor.}}
    0 references
    DLMF id
    DLMF:26.13.E4
    0 references
    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1dec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1bdec
    0 references
    Q12213
    Defining formula
    d ⁢ ( n ) 𝑑 𝑛 {\displaystyle{\displaystyle d(n)}}
    xml-id
    C26.S13.XMD4.m1dec
    0 references
     
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