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A305990
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Expansion of e.g.f.: (1+x) / (exp(-x) - x).
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8
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1, 3, 11, 58, 409, 3606, 38149, 470856, 6641793, 105398650, 1858413061, 36044759796, 762659322385, 17481598316742, 431535346662645, 11413394655983536, 321989729198400385, 9651573930139850610, 306321759739045148293, 10262156907184058219340
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ n! / LambertW(1)^(n+1).
a(n) = Sum_{k=0..n+1} (n+1)!*(n-k+1)^(k-1)/k! for n > 0. - Detlef Meya, Sep 05 2023
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MATHEMATICA
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nmax = 20; CoefficientList[Series[(1+x)/(E^(-x)-x), {x, 0, nmax}], x] * Range[0, nmax]!
a={1}; For[n=1, n<20, n++, AppendTo[a, Sum[(n!)*((n-k+1)^(k-1))*(n+1)/(k!), {k, 0, n+1}]]]; a (* Detlef Meya, Sep 05 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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