I had my first at 35, so put me in the Geriatric Moms category. But my mom turned 39 the day before she had me. My maternal grandmother had 12 kids, and I think at least one or two were "change of life" babies, I think they were called. I believe she was in her early 40s when she had them (and this would be in the 1930s). I do think genetics plays a big role in all of it.
All the women in our family have very short and easy labors. My mom "went natural" back in the 50s before it was fashionable in this country.
You should read Florence King on the subject of "change of life babies". It's a hoot.