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A357322
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Expansion of e.g.f. -LambertW(log(1 - 3*x)/3).
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2
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0, 1, 5, 45, 586, 10024, 213084, 5428072, 161475320, 5501761488, 211466328400, 9057714349672, 428022643010544, 22127292215218072, 1242503403120434168, 75319473068729478360, 4902798528238919060224, 341102498012848479889408
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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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a(n) = Sum_{k=1..n} 3^(n-k) * k^(k-1) * |Stirling1(n,k)|.
a(n) ~ 3^(n - 1/2) * n^(n-1) / ((-1 + exp(3*exp(-1)))^(n - 1/2) * exp(n - 1/2 - 3*n*exp(-1))). - Vaclav Kotesovec, Oct 04 2022
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MATHEMATICA
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With[{m = 20}, Range[0, m]! * CoefficientList[Series[-ProductLog[Log[1 - 3*x]/3], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(log(1-3*x)/3))))
(PARI) a(n) = sum(k=1, n, 3^(n-k)*k^(k-1)*abs(stirling(n, k, 1)));
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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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