DLMF:24.6.E3 (Q7467)

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DLMF:24.6.E3
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    Statements

    Defining formula
    B 2 ⁢ n = ∑ k = 1 n ( k - 1 ) ! ⁢ k ! ( 2 ⁢ k + 1 ) ! ⁢ ∑ j = 1 k ( - 1 ) j - 1 ⁢ ( 2 ⁢ k k + j ) ⁢ j 2 ⁢ n . Bernoulli-number-B 2 𝑛 superscript subscript 𝑘 1 𝑛 𝑘 1 𝑘 2 𝑘 1 superscript subscript 𝑗 1 𝑘 superscript 1 𝑗 1 binomial 2 𝑘 𝑘 𝑗 superscript 𝑗 2 𝑛 {\displaystyle{\displaystyle B_{2n}=\sum_{k=1}^{n}\frac{(k-1)!k!}{(2k+1)!}\*% \sum_{j=1}^{k}(-1)^{j-1}{2k\choose k+j}j^{2n}.}}
    0 references
    DLMF id
    DLMF:24.6.E3
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1abdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1bdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1bdec
    0 references
     
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