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

0,4

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

Prog

(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

Crossrefs

Cf. A001349, A126100.

Sequence in context: A330444 A253949 A336545 * A308478 A157994 A002500

Adjacent sequences: A126098 A126099 A126100 * A126102 A126103 A126104

Keyword

nonn

Author

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

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

Status

approved