A277482 - OEIS

%I #10 Nov 10 2017 07:37:10

%S 0,0,2,9,56,480,5394,75775,1280376,25270056,569899770,14444562803,

%T 406204015524,12545427045008,422007399953398,15354968442741135,

%U 600807449737710832,25153741340051795248,1121917008608064151218,53107023489332468636739,2658946993059795072656540

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

%H G. C. Greubel, <a href="/A277482/b277482.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[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 09 2017

%Y Cf. A000169, A277466, A277473, A277481.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 17 2016