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A308863
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Expansion of e.g.f. (1 + LambertW(-x))/(1 + 2*LambertW(-x)).
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1
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1, 1, 6, 57, 736, 11985, 235296, 5403937, 142073856, 4206560769, 138483596800, 5017244970441, 198363105460224, 8498001799768273, 392127481640165376, 19388814120804416625, 1022681739669784231936, 57317273018414456262273, 3401527253966521309200384
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: 1 / (1 - Sum_{k>=1} k^k*x^k/k!).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k^k * a(n-k).
a(n) ~ sqrt(Pi) * 2^(n - 3/2) * n^(n + 1/2) / exp(n/2). - Vaclav Kotesovec, Jun 29 2019
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MATHEMATICA
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nmax = 18; CoefficientList[Series[(1 + LambertW[-x])/(1 + 2 LambertW[-x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
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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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