OFFSET
1,1
COMMENTS
Replacing 2*n+2 in the formula with m gives the formula to calculate the number of labeled graphs with no isolated nodes of size up to n+1 nodes, using m unique labels (with m > n). An alternative (and much more complicated!) way to find the sequence is with the following recurrence (n>1, m>n): a(n,m)=a(n-1,m)+binomial(m,n)*(-a(n-1,n+1)+sum_{k=1..n*(n+1)/2}binomial(n*(n+1)/2,k)), a(2,m)=binomial(m,2)+binomial(m,3)+binomial(3,2)*binomial(m,3).
FORMULA
a(n)=sum_{k=1..n+1}binomial(2*n+2,k)*A006129(k)
EXAMPLE
a(1)=6 because with 1+1 nodes and 2*1+2 labels, you can construct the following graphs: 1-2, 1-3, 1-4, 2-3, 2-4, 3-4. We have 6 different graphs.
MAPLE
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Delorme C. (delorme(AT)lri.fr), Lopez R. (lopez(AT)lri.fr), Soguet D. (soguet(AT)lri.fr) Jun 08 2006
STATUS
approved