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%I #20 Nov 17 2017 20:05:22
%S 0,1,5,38,422,6184,112632,2453296,62202800,1799623296,58507176320,
%T 2111633645824,83777729991936,3624054557443072,169759643117603840,
%U 8560585769442662400,462387289560368764928,26633435981686107701248,1629609677806398679646208,105555926477075661655441408,7215930505311133152120995840
%N Number of connected functions from {1,2,...,n} into a subset of {1,2,...,n} summed over all subsets.
%H G. C. Greubel, <a href="/A216858/b216858.txt">Table of n, a(n) for n = 0..370</a>
%F E.g.f.: log(1/(1-T(x*exp(x)))) where T(x) is the e.g.f. for A000169.
%F a(n) ~ n!/(2*n*LambertW(exp(-1))^n) * (1 - sqrt(2*(1 + LambertW(exp(-1))) /(Pi*n))/3). - _Vaclav Kotesovec_, Sep 24 2013
%t nn=20; a=-ProductLog[-x Exp[x] ]; Range[0,nn]! CoefficientList[Series[Log[1/(1-a)], {x,0,nn}], x]
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(log(1/(1+ lambertw(-x*exp(x))))))) \\ _G. C. Greubel_, Nov 16 2017
%Y Cf. A216857, A000248, A048802, A072034.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Sep 17 2012
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