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A079571 Number of unlabeled, connected graphs on n vertices whose complements are bipartite.

%I A079571 #18 Sep 18 2019 04:56:32
%S A079571 1,1,1,2,5,11,32,85,299,1115,5474,32298,251129,2527706,33985846,
%T A079571 611846933,14864650916,488222721984,21712049275189,1308300679611460,
%U A079571 106897965189674281,11852113048215107812,1784730721403509209204,365323537513403184463262
%N A079571 Number of unlabeled, connected graphs on n vertices whose complements are bipartite.
%C A079571 Equivalently, number of bipartite graphs whose complement is connected. The only bipartite graphs with disconnected complement are complete bipartite graphs. - _Falk Hüffner_, Jan 22 2016
%H A079571 Andrew Howroyd, <a href="/A079571/b079571.txt">Table of n, a(n) for n = 0..50</a>
%F A079571 a(n) = A033995(n) - floor(n/2).
%t A079571 A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
%t A079571 etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
%t A079571 b = etr[A005142[[# + 1]]&];
%t A079571 a[n_] := b[n] - Floor[n/2];
%t A079571 a /@ Range[0, 50] (* _Jean-François Alcover_, Sep 17 2019 *)
%Y A079571 Cf. A005142, A033995.
%K A079571 nonn
%O A079571 0,4
%A A079571 _Jim Nastos_, Jan 24 2003
%E A079571 Corrected and extended using formula by _Falk Hüffner_, Jan 22 2016
%E A079571 a(0)=1 prepended and terms a(21) and beyond from _Andrew Howroyd_, Sep 05 2018