|
%I #16 Nov 14 2014 10:34:33
%S 1,1,3,15,121,1665,43883,2437423,289320049,71423435521,35912764315347,
%T 36427941634714575,74226534887938021609,303199273967377493113473,
%U 2480131664037469755458069819,40602053121132407513785975382767,1329877926764331449042460153768864481
%N Exponential transform of A006125.
%C 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).
%H Alois P. Heinz, <a href="/A197505/b197505.txt">Table of n, a(n) for n = 0..50</a>
%F 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.
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(binomial(n-1, j-1) *2^(j*(j-1)/2) *a(n-j), j=1..n))
%p end:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Oct 16 2011
%t a=Sum[2^Binomial[n,2] x^n/n!,{n,0,20}]; Range[0,20]! CoefficientList[Series[Exp[a-1],{x,0,20}],x]
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Oct 15 2011
|
