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DLMF:26.14.E16

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Formula:8660
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MaRDI QIDQ8660

  • Label: DLMF:26.14.E16


Digital Library of Mathematical Functions ID 26.14.E16

⟨ n 2 ⟩ = 3 n - ( n + 1 ) ⁒ 2 n + ( n + 1 2 ) , Eulerian-number 𝑛 2 superscript 3 𝑛 𝑛 1 superscript 2 𝑛 binomial 𝑛 1 2 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{n}{2}=3^{n}-(n+1)2^{n}+% \genfrac{(}{)}{0.0pt}{}{n+1}{2},}}


Constraint(s)

n β‰₯ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}

Symbols List

  • ⟨ n k ⟩ Eulerian-number 𝑛 π‘˜ {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}} :
  • ( m n ) binomial π‘š 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}} :
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
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