DLMF:24.15.E11 (Q7568)

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DLMF:24.15.E11
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    Statements

    Defining formula
    ∑ k = 0 ⌊ n / 2 ⌋ ( n 2 ⁢ k ) ⁢ ( 5 9 ) k ⁢ B 2 ⁢ k ⁢ u n - 2 ⁢ k = n 6 ⁢ v n - 1 + n 3 n ⁢ v 2 ⁢ n - 2 , superscript subscript 𝑘 0 𝑛 2 binomial 𝑛 2 𝑘 superscript 5 9 𝑘 Bernoulli-number-B 2 𝑘 subscript 𝑢 𝑛 2 𝑘 𝑛 6 subscript 𝑣 𝑛 1 𝑛 superscript 3 𝑛 subscript 𝑣 2 𝑛 2 {\displaystyle{\displaystyle\sum_{k=0}^{\left\lfloor\ifrac{n}{2}\right\rfloor}% {n\choose 2k}\left(\frac{5}{9}\right)^{k}B_{2k}u_{n-2k}=\frac{n}{6}v_{n-1}+% \frac{n}{3^{n}}v_{2n-2},}}
    0 references
    DLMF id
    DLMF:24.15.E11
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1agdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1cdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1kdec
    0 references
    Q12133
    Defining formula
    u n subscript 𝑢 𝑛 {\displaystyle{\displaystyle u_{n}}}
    xml-id
    C24.S15.XMD3.m1dec
    0 references
    Q12134
    Defining formula
    v n subscript 𝑣 𝑛 {\displaystyle{\displaystyle v_{n}}}
    xml-id
    C24.S15.XMD4.m1dec
    0 references
     
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