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%I #9 Oct 30 2020 02:32:32
%S 1,0,-1,-2,0,16,50,-132,-2184,-9984,6912,341760,38544,-47086272,
%T -702019344,-6076389984,-43980940800,-656377887744,-16782743357568,
%U -368775477229824,-6770025717901056,-118247220867640320,-2271088046291742720,-50203882870716579840
%N E.g.f.: 1 / (1 - x - log(1 - x)).
%F a(0) = 1; a(n) = -Sum_{k=2..n} binomial(n,k) * (k-1)! * a(n-k).
%F 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
%t nmax = 23; CoefficientList[Series[1/(1 - x - Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%t 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}]
%o (PARI) my(x='x + O('x^30)); Vec(serlaplace(1/(1 - x - log(1 - x)))) \\ _Michel Marcus_, Oct 29 2020
%Y Cf. A006252, A089148, A226226.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Oct 28 2020
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