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A317632 Number of connected induced nonempty non-singleton subgraphs of labeled connected graphs with n vertices.

%I A317632 #11 Dec 10 2018 16:43:55
%S A317632 0,0,1,13,294,12198,946712,140168924,40223263760,22598607583376,
%T A317632 24999757695984960,54630901092648916704,236304498092496715916416,
%U A317632 2026201628540583716863002880,34482826679730591694177065948928,1166004710785628820717860509317415168
%N A317632 Number of connected induced nonempty non-singleton subgraphs of labeled connected graphs with n vertices.
%C A317632 The edges of an induced subgraph G|S are those edges of G with both ends contained in S, where S is a subset of the vertices.
%H A317632 Andrew Howroyd, <a href="/A317632/b317632.txt">Table of n, a(n) for n = 0..50</a>
%H A317632 Gus Wiseman, <a href="/A317632/a317632.png">All 294 connected induced subgraphs of labeled connected graphs with 4 vertices.</a>
%o A317632 (PARI)
%o A317632 seq(n)={
%o A317632   my(p=sum(k=0, n, 2^binomial(k, 2)*x^k/k!, O(x*x^n)));
%o A317632   my(g=Vec(serlaplace(log(p))));
%o A317632   my(q=sum(k=0, n, sum(j=2, k, binomial(k,j)*g[j]*2^(binomial(k-j, 2) + j*(k-j)))*x^k/k!, O(x*x^n)));
%o A317632   Vec(serlaplace(q/p), -n-1)
%o A317632 } \\ _Andrew Howroyd_, Dec 10 2018
%Y A317632 Cf. A001187, A006125, A048143, A293510, A304717, A317631, A317634, A317635.
%K A317632 nonn
%O A317632 0,4
%A A317632 _Gus Wiseman_, Aug 02 2018
%E A317632 a(6) from _Gus Wiseman_, Dec 10 2018
%E A317632 Terms a(7) and beyond from _Andrew Howroyd_, Dec 10 2018