cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A126101 #16 Jan 24 2022 07:57:39
%S A126101 1,1,1,2,8,44,333,3771,67141,2027119,108880264,10682138680,
%T A126101 1933264826485,648235902085512,404043306773404163,
%U A126101 469727521267710406698,1022090075330054063050850,4176738163895992397728030132,32159402671814249205978139454278,467987765188007308268883267776373304
%N A126101 Number of connected unlabeled graphs on n nodes that are rooted at a non-cut node.
%C A126101 Same as A126100 except that the root node may not be a cut node, i.e., a node whose removal would disconnect the graph.
%H A126101 Andrew Howroyd, <a href="/A126101/b126101.txt">Table of n, a(n) for n = 0..50</a>
%o A126101 (PARI) \\ See A126100 for g; InvEulerT takes inverse Euler transform.
%o A126101 InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v,n,polcoef(p,n)), vector(#v,n,1/n))}
%o A126101 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
%Y A126101 Cf. A001349, A126100.
%K A126101 nonn
%O A126101 0,4
%A A126101 _David Applegate_ and _N. J. A. Sloane_, Mar 06 2007
%E A126101 a(6)-a(10) computed by _Gordon F. Royle_, Mar 05 2007
%E A126101 a(11)-a(19) computed by _David Applegate_ from A126100, Mar 07 2007
%E A126101 a(15)-a(18) corrected and terms a(20) and beyond from _Andrew Howroyd_, Nov 23 2020