A216858 Number of connected functions from {1,2,...,n} into a subset of {1,2,...,n} summed over all subsets.
0, 1, 5, 38, 422, 6184, 112632, 2453296, 62202800, 1799623296, 58507176320, 2111633645824, 83777729991936, 3624054557443072, 169759643117603840, 8560585769442662400, 462387289560368764928, 26633435981686107701248, 1629609677806398679646208, 105555926477075661655441408, 7215930505311133152120995840
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..370
Programs
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Mathematica
nn=20; a=-ProductLog[-x Exp[x] ]; Range[0,nn]! CoefficientList[Series[Log[1/(1-a)], {x,0,nn}], x] -
PARI
x='x+O('x^30); concat([0], Vec(serlaplace(log(1/(1+ lambertw(-x*exp(x))))))) \\ G. C. Greubel, Nov 16 2017
Formula
E.g.f.: log(1/(1-T(x*exp(x)))) where T(x) is the e.g.f. for A000169.
a(n) ~ n!/(2*n*LambertW(exp(-1))^n) * (1 - sqrt(2*(1 + LambertW(exp(-1))) /(Pi*n))/3). - Vaclav Kotesovec, Sep 24 2013