DLMF:24.6.E3 (Q7467)

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DLMF:24.6.E3
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    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}.}}
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    DLMF:24.6.E3
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