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A338448
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E.g.f.: 1 / (1 - x - log(1 - x)).
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1
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1, 0, -1, -2, 0, 16, 50, -132, -2184, -9984, 6912, 341760, 38544, -47086272, -702019344, -6076389984, -43980940800, -656377887744, -16782743357568, -368775477229824, -6770025717901056, -118247220867640320, -2271088046291742720, -50203882870716579840
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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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a(0) = 1; a(n) = -Sum_{k=2..n} binomial(n,k) * (k-1)! * a(n-k).
a(n) ~ -n! / (n * log(n)^2) * (1 - 2*gamma/log(n) + (3*gamma^2 - Pi^2/2)/log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 29 2020
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MATHEMATICA
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nmax = 23; CoefficientList[Series[1/(1 - x - Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 23}]
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PROG
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(PARI) my(x='x + O('x^30)); Vec(serlaplace(1/(1 - x - log(1 - x)))) \\ Michel Marcus, Oct 29 2020
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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