DLMF:24.6.E6 (Q7470)

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DLMF:24.6.E6
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    Statements

    test
    E 2 ⁢ n = ∑ k = 1 2 ⁢ n ( - 1 ) k 2 k - 1 ⁢ ( 2 ⁢ n + 1 k + 1 ) ⁢ ∑ j = 0 ⌊ 1 2 ⁢ k - 1 2 ⌋ ( k j ) ⁢ ( k - 2 ⁢ j ) 2 ⁢ n . Euler-number-E 2 𝑛 superscript subscript 𝑘 1 2 𝑛 superscript 1 𝑘 superscript 2 𝑘 1 binomial 2 𝑛 1 𝑘 1 superscript subscript 𝑗 0 1 2 𝑘 1 2 binomial 𝑘 𝑗 superscript 𝑘 2 𝑗 2 𝑛 {\displaystyle{\displaystyle E_{2n}=\sum_{k=1}^{2n}\frac{(-1)^{k}}{2^{k-1}}{2n% +1\choose k+1}\*\sum_{j=0}^{\left\lfloor\tfrac{1}{2}k-\tfrac{1}{2}\right% \rfloor}{k\choose j}(k-2j)^{2n}.}}
    0 references
    DLMF id
    DLMF:24.6.E6
    0 references
    Symbols used
    Q11238
    test
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1abdec
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