It's not that hard of a calculation, with the exception of following the Colony / Shelters rule properly.

C = total number of kingdom card piles

T = total number of kingdom card piles costing _{} or less

E = total number of events + landmarks

Non-Young Witch games:

((C-1) Choose 10) +

((C-1) Choose 10) * (E) +

((C-1) Choose 10) * (E Choose 2)

+

Young Witch games:

(C-1) Choose 9) * T +

(C-1) Choose 9) * T * (E) +

(C-1) Choose 9) * T * (E Choose 2)

An upper bound would be to multiply it by 4 for the Shelters / Colonies. Also, my calculation isn't accounting for the fact that there's fewer bane choices when the Kingdom already has cards that cost _{} or less.

*Edit* I suppose you need to calculate Kingdoms that contain Obelisk separately; those ones are just multiplied by 10.