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%I #19 Nov 13 2017 02:50:03
%S 0,1,-2,18,-144,1900,-26820,485394,-9679936,225394488,-5765768100,
%T 164923889350,-5132384691984,174433050454260,-6385752833589220,
%U 251596880714336850,-10585338808667808000,474507594337155230704,-22550580127644413987268
%N a(n) = n! * [x^n] -exp(-n*x)*LambertW(-x).
%C The n-th term of the n-th inverse binomial transform of A000169 (with A000169(0) = 0).
%H G. C. Greubel, <a href="/A290215/b290215.txt">Table of n, a(n) for n = 0..385</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) ~ -(-1)^n * LambertW(1) * n^n. - _Vaclav Kotesovec_, Oct 06 2017
%t Table[n! SeriesCoefficient[-Exp[-n x] LambertW[-x], {x, 0, n}], {n, 0, 18}]
%t Table[Sum[(-n)^(n - k) Binomial[n, k] k^(k - 1), {k, 1, n}], {n, 0, 18}]
%Y Cf. A000169, A277474, A292633.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Oct 06 2017
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