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DLMF:24.6.E5

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Formula:8162
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MaRDI QIDQ8162

  • Label: DLMF:24.6.E5


Digital Library of Mathematical Functions ID 24.6.E5

E 2 ⁢ n = 1 2 n - 1 ⁢ ∑ k = 0 n - 1 ( - 1 ) n - k ⁢ ( n - k ) 2 ⁢ n ⁢ ∑ j = 0 k ( 2 ⁢ n - 2 ⁢ j k - j ) ⁢ 2 j , Euler-number-E 2 𝑛 1 superscript 2 𝑛 1 superscript subscript 𝑘 0 𝑛 1 superscript 1 𝑛 𝑘 superscript 𝑛 𝑘 2 𝑛 superscript subscript 𝑗 0 𝑘 binomial 2 𝑛 2 𝑗 𝑘 𝑗 superscript 2 𝑗 {\displaystyle{\displaystyle E_{2n}=\frac{1}{2^{n-1}}\sum_{k=0}^{n-1}(-1)^{n-k% }(n-k)^{2n}\*\sum_{j=0}^{k}{2n-2j\choose k-j}2^{j},}}


Constraint(s)

Symbols List

  • E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}} :
  • ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}} :
  • j 𝑗 {\displaystyle{\displaystyle j}} : integer
  • k 𝑘 {\displaystyle{\displaystyle k}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
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