OFFSET
0,2
COMMENTS
The null graph is considered to be a connected graph.
a(n)/(2^n * 2^binomial(n,2)) is the probability that a random subset of vertices chosen from a random graph will induce a connected subgraph. This probability is a minimum at n=7 and approaches 1 as n gets big.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..81
FORMULA
a(n) = Sum_{j=0..n} A001187(j)/2^binomial(j,2) * binomial(n,j) * 2^binomial(n,2).
MATHEMATICA
nn = 15; A[z_] := Sum[2^Binomial[n, 2] z^n/n!, {n, 0, nn}]; list = Range[0, nn]! CoefficientList[Series[Log[A[z]] + 1, {z, 0, nn}], z]; Table[ Sum[list[[i]]/2^Binomial[i - 1, 2] Binomial[n, i - 1] 2^ Binomial[n, 2], {i, 1, Length[list]}], {n, 0, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 12 2017
STATUS
approved