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A323673
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Expansion of e.g.f. log(1 - LambertW(-x)*(2 + LambertW(-x))/2).
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2
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0, 1, 0, 2, 7, 69, 696, 9400, 148506, 2753793, 58255840, 1388008566, 36768832200, 1072407094693, 34151921130432, 1179292944433500, 43892264744070736, 1751768399754149025, 74633720517351765504, 3380997879130123703818, 162286529338732345488000, 8227876237310253918100581
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: log(1 + Sum_{k>=1} k^(k-2)*x^k/k!).
a(0) = 0; a(n) = A000272(n) - (1/n)*Sum_{k=1..n-1} binomial(n,k)*A000272(n-k)*k*a(k).
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MAPLE
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seq(n!*coeff(series(log(1-LambertW(-x)*(2+LambertW(-x))/2), x=0, 22), x, n), n=0..21); # Paolo P. Lava, Jan 28 2019
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MATHEMATICA
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nmax = 21; CoefficientList[Series[Log[1 - LambertW[-x] (2 + LambertW[-x])/2], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = n^(n - 2) - Sum[Binomial[n, k] (n - k)^(n - k - 2) k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 21}]
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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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