%I #12 Jun 22 2017 06:05:43
%S 0,1,1,5,26,224,2244,28496,417976,7122384,136770960,2937770472,
%T 69626588976,1806936836184,50936933449752,1550292926398680,
%U 50661309325357824,1769286989373994752,65762170385201959680,2591979585702305271552,107982615297265761991680
%N E.g.f.: -LambertW(-log(1+x)).
%H G. C. Greubel, <a href="/A277489/b277489.txt">Table of n, a(n) for n = 0..395</a>
%F a(n) = Sum_{k=1..n} Stirling1(n, k)*k^(k-1).
%F a(n) ~ (exp(exp(-1))-1)^(1/2-n) * exp(-exp(-1)/2+1/2-n) * n^(n-1).
%t CoefficientList[Series[-LambertW[-Log[1+x]], {x, 0, 20}], x] * Range[0, 20]!
%t Table[Sum[StirlingS1[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-log(1+x))))) \\ _G. C. Greubel_, Jun 21 2017
%Y Cf. A001865, A052807, A133297.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Oct 17 2016
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