Counting homomorphisms in plain exponential time

In the counting Graph Homomorphism problem GraphHOM the question is: Given graphs G, H, find the number of homomorphisms from G to H. This problem is generally #P-complete, moreover, Cygan et al. proved that unless the Exponential Time Hypothesis fails there is no algorithm that solves this problem in plain exponential time. This, however, does not rule out the possibility that faster algorithms exist for restricted problems of this kind. Wahlstrom proved that #GraphHOM can be solved in plain exponential time, provided H has clique width k. We generalize this result to a larger class of graphs, and also identify several other graph classes that admit a plain exponential algorithm for # GraphHOM.