Where will we sit?

Discrete Mathematics Level pending

There are 40 persons and 4 big boggies numbered 1,2,3,4. The persons have to be sited into them such that no boggy is left empty and number of persons in those are in A.P. what is the number of possible arrangement? The answer is expressible in form of ({n!×a!}/{b!c!d!e!}+a!/(f!)^g).find the sum of all constants in the answer.

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