A126101 Number of connected unlabeled graphs on n nodes that are rooted at a non-cut node.

1, 1, 1, 2, 8, 44, 333, 3771, 67141, 2027119, 108880264, 10682138680, 1933264826485, 648235902085512, 404043306773404163, 469727521267710406698, 1022090075330054063050850, 4176738163895992397728030132, 32159402671814249205978139454278, 467987765188007308268883267776373304

Offset: 0

Author

David Applegate and N. J. A. Sloane, Mar 06 2007

Keywords

• nonn

Comments

Same as A126100 except that the root node may not be a cut node, i.e., a node whose removal would disconnect the graph.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A001349, A126100.

Programs

PARI

\\ See A126100 for g; InvEulerT takes inverse Euler transform.
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v,n,polcoef(p,n)), vector(#v,n,1/n))}
seq(n)={concat([1, 1], InvEulerT(Vec(-1+Ser(vector(n, n, g(n-1, 1)))/Ser(vector(n, n, g(n-1, 0))))))} \\ Andrew Howroyd, Nov 23 2020

Extensions

a(6)-a(10) computed by Gordon F. Royle, Mar 05 2007

a(11)-a(19) computed by David Applegate from A126100, Mar 07 2007

a(15)-a(18) corrected and terms a(20) and beyond from Andrew Howroyd, Nov 23 2020