OFFSET
0,3
COMMENTS
a(n) is the number of simple labeled graphs on n nodes where the nodes are divided into any number of groups and no edge connects nodes of different groups. (Nodes within a group are not necessarily connected).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..50
FORMULA
E.g.f.: exp(A(x)-1) where A(x) = Sum_{n>=0} 2^C(n,2) x^n/n! is the e.g.f. of A006125.
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1) *2^(j*(j-1)/2) *a(n-j), j=1..n))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Oct 16 2011
MATHEMATICA
a=Sum[2^Binomial[n, 2] x^n/n!, {n, 0, 20}]; Range[0, 20]! CoefficientList[Series[Exp[a-1], {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 15 2011
STATUS
approved