DLMF:24.6.E4 (Q7468)

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DLMF:24.6.E4
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    Statements

    Defining formula
    E 2 ⁢ n = ∑ k = 1 n 1 2 k - 1 ⁢ ∑ j = 1 k ( - 1 ) j ⁢ ( 2 ⁢ k k - j ) ⁢ j 2 ⁢ n , Euler-number-E 2 𝑛 superscript subscript 𝑘 1 𝑛 1 superscript 2 𝑘 1 superscript subscript 𝑗 1 𝑘 superscript 1 𝑗 binomial 2 𝑘 𝑘 𝑗 superscript 𝑗 2 𝑛 {\displaystyle{\displaystyle E_{2n}=\sum_{k=1}^{n}\frac{1}{2^{k-1}}\sum_{j=1}^% {k}(-1)^{j}{2k\choose k-j}j^{2n},}}
    0 references
    DLMF id
    DLMF:24.6.E4
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1adec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1cdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1cdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
    0 references
     
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