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DLMF:26.14.E16 - MaRDI portal

DLMF:26.14.E16 (Q8660)

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DLMF:26.14.E16
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    Statements

    DLMF defining formula
    ⟨ 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},}}
    0 references
    constraint
    n ≥ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
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    Symbols used
    Q12220
    DLMF defining formula
    ⟨ n k ⟩ Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    xml-id
    C26.S14.SS1.p3.m2amdec
    0 references
    Q10728
    DLMF defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1addec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1ndec
    0 references

    Identifiers

     
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