A069831 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.

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, 279, 354, 422, 524, 627, 780, 926, 1134, 1355, 1651, 1958, 2366, 2809, 3372, 3988, 4757, 5628, 6678, 7874, 9283, 10964, 12861, 15130, 17686, 20799, 24209, 28389