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DLMF:1.2.E5 - MaRDI portal

DLMF:1.2.E5 (Q5)

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DLMF:1.2.E5
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    Statements

    DLMF defining formula
    ( n 0 ) + ( n 2 ) + ( n 4 ) + … + ( n ℓ ) = 2 n - 1 , binomial 𝑛 0 binomial 𝑛 2 binomial 𝑛 4 … binomial 𝑛 ℓ superscript 2 𝑛 1 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{0}+\genfrac{(}{)}{0.0pt% }{}{n}{2}+\genfrac{(}{)}{0.0pt}{}{n}{4}+\dots+\genfrac{(}{)}{0.0pt}{}{n}{\ell}% =2^{n-1},}}
    0 references
    Symbols used
    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
    integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C1.S1.XMD5.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1ddec
    0 references

    Identifiers

     
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