DLMF:24.6.E12 (Q7476)

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DLMF:24.6.E12
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    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}.}}
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    DLMF:24.6.E12
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