chess board layouts

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I have been trying to find information on the total possible layouts in chess. I know this is going to be a huge number and a few sites even claim to show it. none of these sites show any of their math involved. So far here is what i have: 13 types og pieces(6 of each color plus no piece) 64 squares. this gives me 13^64 the first row and last row can not be pawns due to promotion. changing it to (11^16)*(13^48) this can be further reduced to (((11*11)-4)^8) * (((13*13)-4)^24) by eleminating most of the king side by side. I will expand on this more later hopefully someone else will have some ideas.