DLMF:24.6.E12 (Q7476)

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DLMF:24.6.E12
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    Statements

    Defining formula
    E 2 ⁢ n = ∑ k = 0 2 ⁢ n 1 2 k ⁢ ∑ j = 0 k ( - 1 ) j ⁢ ( k j ) ⁢ ( 1 + 2 ⁢ j ) 2 ⁢ n . Euler-number-E 2 𝑛 superscript subscript 𝑘 0 2 𝑛 1 superscript 2 𝑘 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑘 𝑗 superscript 1 2 𝑗 2 𝑛 {\displaystyle{\displaystyle E_{2n}=\sum_{k=0}^{2n}\frac{1}{2^{k}}\sum_{j=0}^{% k}(-1)^{j}{k\choose j}(1+2j)^{2n}.}}
    0 references
    DLMF id
    DLMF:24.6.E12
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1addec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1akdec
    0 references
     
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