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Formula:8153

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Digital Library of Mathematical Functions ID 24.5.E8

∑ k = 0 n 2 2 ⁢ k ⁢ B 2 ⁢ k ( 2 ⁢ k ) ! ⁢ ( 2 ⁢ n + 1 - 2 ⁢ k ) ! = 1 ( 2 ⁢ n ) ! , superscript subscript 𝑘 0 𝑛 superscript 2 2 𝑘 Bernoulli-number-B 2 𝑘 2 𝑘 2 𝑛 1 2 𝑘 1 2 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n}\frac{2^{2k}B_{2k}}{(2k)!(2n+1-2k)!}% =\frac{1}{(2n)!},}}


Constraint(s)

n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • ! {\displaystyle{\displaystyle!}} :
  • k 𝑘 {\displaystyle{\displaystyle k}} : 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 10:02.
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