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A126101
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Number of connected unlabeled graphs on n nodes that are rooted at a non-cut node.
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2
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1, 1, 1, 2, 8, 44, 333, 3771, 67141, 2027119, 108880264, 10682138680, 1933264826485, 648235902085512, 404043306773404163, 469727521267710406698, 1022090075330054063050850, 4176738163895992397728030132, 32159402671814249205978139454278, 467987765188007308268883267776373304
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OFFSET
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0,4
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COMMENTS
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Same as A126100 except that the root node may not be a cut node, i.e., a node whose removal would disconnect the graph.
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(15)-a(18) corrected and terms a(20) and beyond from Andrew Howroyd, Nov 23 2020
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STATUS
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approved
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