DLMF:24.15.E8 (Q7565)

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DLMF:24.15.E8
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    Statements

    test
    ∑ k = 0 n ( - 1 ) n + k ⁢ s ⁡ ( n + 1 , k + 1 ) ⁢ B k = n ! n + 1 . superscript subscript 𝑘 0 𝑛 superscript 1 𝑛 𝑘 Stirling-number-first-kind-S 𝑛 1 𝑘 1 Bernoulli-number-B 𝑘 𝑛 𝑛 1 {\displaystyle{\displaystyle\sum_{k=0}^{n}(-1)^{n+k}s\left(n+1,k+1\right)B_{k}% =\frac{n!}{n+1}.}}
    0 references
    DLMF id
    DLMF:24.15.E8
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    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1addec
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    Q12132
    test
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5adec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
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    Q12113
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1bdec
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    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1hdec
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