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

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..370

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

Mathematica

nn=20; a=-ProductLog[-x Exp[x] ]; Range[0, nn]! CoefficientList[Series[Log[1/(1-a)], {x, 0, nn}], x]

Prog

(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(log(1/(1+ lambertw(-x*exp(x))))))) \\ G. C. Greubel, Nov 16 2017

Crossrefs

Cf. A216857, A000248, A048802, A072034.

Sequence in context: A371342 A069471 A355788 * A338867 A110467 A379861

Adjacent sequences: A216855 A216856 A216857 * A216859 A216860 A216861

Keyword

nonn

Author

Geoffrey Critzer, Sep 17 2012

Status

approved