DLMF:8.11.E16 (Q2589)

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DLMF:8.11.E16
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    Defining formula
    S n ⁢ ( 1 ) - 1 2 ⁢ n ! ⁢ e n n n ∼ - 2 3 + 4 135 ⁢ n - 1 - 8 2835 ⁢ n - 2 - 16 8505 ⁢ n - 3 + … , asymptotic-expansion subscript 𝑆 𝑛 1 1 2 𝑛 superscript 𝑒 𝑛 superscript 𝑛 𝑛 2 3 4 135 superscript 𝑛 1 8 2835 superscript 𝑛 2 16 8505 superscript 𝑛 3 … {\displaystyle{\displaystyle S_{n}(1)-\frac{1}{2}\frac{n!e^{n}}{n^{n}}\sim-% \tfrac{2}{3}+\tfrac{4}{135}n^{-1}-\tfrac{8}{2835}n^{-2}-\tfrac{16}{8505}n^{-3}% +\dots,}}
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    DLMF id
    DLMF:8.11.E16
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