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%I #6 May 25 2024 23:47:48
%S 1,0,0,1,1,1,2,3,3,5,8,10,13,16,22,29,36,45,61,74,95,118,152,183,232,
%T 279,354,422,524,627,780,926,1134,1355,1651,1958,2366,2809,3372,3988,
%U 4757,5628,6678,7874,9283,10964,12861,15130,17686,20799,24209,28389
%N Number of graphical partitions of simple Eulerian graphs (partitions given by the degrees of vertices of simple (no loops or multiple edges) graphs having only vertices of even degrees) having n edges.
%H Sean A. Irvine, <a href="/A069831/b069831.txt">Table of n, a(n) for n = 0..100</a>
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a069/A069831.java">Java program</a> (github)
%e a(1)=a(2)=0 since Eulerian graphs having 1 or 2 edges are not simple. The triangle is the unique Eulerian graph having 3 edges and no isolated vertices, thus showing a(3)=1.
%Y Cf. A000569.
%K nonn
%O 0,7
%A _Roland Bacher_, Apr 23 2002