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Formula:8246

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Digital Library of Mathematical Functions ID 24.14.E8

∑ ( 2 ⁢ n ) ! ( 2 ⁢ j ) ! ⁢ ( 2 ⁢ k ) ! ⁢ ( 2 ⁢ ℓ ) ! ⁢ B 2 ⁢ j ⁢ B 2 ⁢ k ⁢ B 2 ⁢ ℓ = ( n - 1 ) ⁢ ( 2 ⁢ n - 1 ) ⁢ B 2 ⁢ n + n ⁢ ( n - 1 2 ) ⁢ B 2 ⁢ n - 2 , 2 𝑛 2 𝑗 2 𝑘 2 ℓ Bernoulli-number-B 2 𝑗 Bernoulli-number-B 2 𝑘 Bernoulli-number-B 2 ℓ 𝑛 1 2 𝑛 1 Bernoulli-number-B 2 𝑛 𝑛 𝑛 1 2 Bernoulli-number-B 2 𝑛 2 {\displaystyle{\displaystyle\sum\frac{(2n)!}{(2j)!(2k)!(2\ell)!}B_{2j}B_{2k}B_% {2\ell}=(n-1)(2n-1)B_{2n}+n(n-\tfrac{1}{2})B_{2n-2},}}


Constraint(s)

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • ! {\displaystyle{\displaystyle!}} :
  • j 𝑗 {\displaystyle{\displaystyle j}} : integer
  • k 𝑘 {\displaystyle{\displaystyle k}} : integer
  • ℓ ℓ {\displaystyle{\displaystyle\ell}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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