DLMF:26.8.E36 (Q7864)

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DLMF:26.8.E36
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    Statements

    Defining formula
    ∑ k = 0 n ( - 1 ) n - k ⁢ k ! ⁢ S ⁡ ( n , k ) = 1 . superscript subscript 𝑘 0 𝑛 superscript 1 𝑛 𝑘 𝑘 Stirling-number-second-kind-S 𝑛 𝑘 1 {\displaystyle{\displaystyle\sum_{k=0}^{n}(-1)^{n-k}k!S\left(n,k\right)=1.}}
    0 references
    DLMF id
    DLMF:26.8.E36
    0 references
    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.m2asdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5akdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1addec
    0 references
     
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