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I want to find the sum of the reciprocals of the factorials of the elements of in the sets [[0,2,3,0,0], [2,3,0,0,0], [1,1,2,2,0] .....]]  -----(1)

For example 1/(0!2!3!0!0!) + 1/(2!3!0!0!)+ 1/(1!1!2!2!0!)+........;----(2)

The lists are the partion(5) made into a list of 5 elements with 0s filling the partitions with less than 5 elemenst such as (2,2,1)=>(2,2,1,0,0)

All I need is help on how to make from (1) the sum (2) which is the sum of the reciprocals of the products of the factorials of each set.