SOLVED. Crime/Detective novel, first in series. Older PI asked to find out if deaths in a group of older people who meet once a year is suspicious. [s]

[Vincent]

I think it's an American novel - possibly set in New York. It's about a private detective, and I think it's the first book in a series about this PI. He's an older man, I think has a fling with a younger woman, drinks etc
In the story, a man visits the PI and tells him about a group or club that he is part of. This group meets once a year, or decade (can't remember) just to meet up, talk, and see how their lives are going. They are a group of older people, so the man would expect some of them to pass away, but he thinks that more people have died than is statistically likely and wonders if someone is knocking them off one by one and making in look non-suspicious. He asks the private detective to look into whether it really is just chance, or if there is something else going on.
I read it about 10-15 years ago. So 2000-2006 time. And it was a paperback, so probably had been published some time before that. However, I don't remember it being particuarly old fashioned. I know one of the characters had fought in Vietnam some decades before so it might well be a 1990s or 2000s novel.
Thanks!

[Kate]

bumping because I'd love to read this once it is found.

[Kym]

A Long Line of Dead Men by Lawrence Block ?

[Vincent]

Yes! Thank you. Sounds perfect and the cover also looks familiar. The only thing that's different is that I thought the one I read was the first in a series, but I'm sure I'm mistaken about that.
Thanks Kym, good knowledge.

[Kym]

You're welcome Vincent.