Y = 2(G-G0)α
where Y is the observed number of kids for each generation and α is the average number of kids per family while the assumption that it's constant across generations. Since we're dealing with a comparatively closed population that is also overwhelmingly agrarian over 350 of the last 400 years, that's probably OK.
Here's the fun geeky part. In logarithmic space, that's:
log Y = (G-G0) log 2 + log α
So borrowing the data from the last posting for Generations 3 through 10 (so G0 = 3), we can get the average for log α (0.766) and for extra geekiness, the distribution about that mean to get the standard deviation (0.143) which corresponds to:
α = 5.8 ± 1.9
So, on average 4 to 8 children in each family!