A197505 Exponential transform of A006125.

1, 1, 3, 15, 121, 1665, 43883, 2437423, 289320049, 71423435521, 35912764315347, 36427941634714575, 74226534887938021609, 303199273967377493113473, 2480131664037469755458069819, 40602053121132407513785975382767, 1329877926764331449042460153768864481

Offset: 0

Author

Geoffrey Critzer, Oct 15 2011

Keywords

• nonn

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

Programs

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]

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.