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E.g.f.: -log(1+x)*LambertW(-x).
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%I #9 Nov 10 2017 07:37:03

%S 0,0,2,3,32,240,3114,44065,777720,15582168,357427770,9151281293,

%T 259607392164,8070381333872,272960010908662,9976300661919345,

%U 391837137436921072,16458193396472517328,736145006794621566642,34932117830021859779517,1752782822664497750549660

%N E.g.f.: -log(1+x)*LambertW(-x).

%H G. C. Greubel, <a href="/A277481/b277481.txt">Table of n, a(n) for n = 0..385</a>

%F a(n) ~ log(1+exp(-1)) * n^(n-1).

%t CoefficientList[Series[-Log[1+x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!

%t Table[n!*Sum[(-1)^(n-k-1)*k^(k-1)/(k!*(n-k)), {k, 1, n-1}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 28 2016 *)

%o (PARI) x='x+O('x^50); concat([0,0], Vec(serlaplace(-log(1+x)*lambertw(-x) ))) \\ _G. C. Greubel_, Nov 08 2017

%Y Cf. A000169, A277465, A277473, A277482.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 17 2016