cp's OEIS Frontend

A273256 Number of simple labeled graphs on n vertices with at most one nontrivial component and all vertex degrees are even.

%I A273256 #12 Aug 28 2016 17:58:43
%S A273256 1,1,1,2,8,64,1014,32593,2093589,268333725,68714765337,35183979518038,
%T A273256 36028733659454920,73786955927716463496,302231441864128208088266,
%U A273256 2475880062024448199702310129,40564819165779582804001294004849,1329227995578862816338009185350962977,87112285929737129482236375622145146977689
%N A273256 Number of simple labeled graphs on n vertices with at most one nontrivial component and all vertex degrees are even.
%C A273256 Some graph theory texts call these graphs Eulerian.  Cf. A033678.
%D A273256 D. B. West, Introduction to Graph Theory, 2nd edition, Pearson Education, 2001, page 27.
%F A273256 E.g.f.: exp(x)*(log(A(x) + 1) - x + 1) where A(x) = Sum_{n>=1} 2^binomial(n-1,2)x^n/n!.
%e A273256 a(4) = 8 because there are 1+4+3=8 labelings on these three graphs
%e A273256 1)
%e A273256 o o
%e A273256 o o
%e A273256 2)
%e A273256 o-o
%e A273256 |/
%e A273256 o o
%e A273256 3)
%e A273256 o-o
%e A273256 | |
%e A273256 o-o
%t A273256 nn = 18; Clear[g];g[z_] := Sum[2^Binomial[n - 1, 2] z^n/n!, {n, 1, nn}];Range[0, nn]! CoefficientList[Series[Exp[z] (Log[g[z] + 1] - z + 1), {z, 0, nn}], z]
%K A273256 nonn
%O A273256 0,4
%A A273256 _Geoffrey Critzer_, Aug 28 2016