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A126101 Number of connected unlabeled graphs on n nodes that are rooted at a non-cut node. 2
1, 1, 1, 2, 8, 44, 333, 3771, 67141, 2027119, 108880264, 10682138680, 1933264826485, 648235902085512, 404043306773404163, 469727521267710406698, 1022090075330054063050850, 4176738163895992397728030132, 32159402671814249205978139454278, 467987765188007308268883267776373304 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)