Question: Invert a summation?

I need the formal solution to the inverse of (d(m) = sum of c(k)/(k-m)! from k = m+1 to j  for all m from 0 through j-1). Egorychev's theory of turning summations into complex integrals seems to work only on his chosen examples, namely, where the summation index, k, is the lower variable in the binomial coefficient, not the upper variables as in my case k-choose-m, if one redefines c(k) as c(k)*k! and d(m) as d(m)*m!  Any ideas?  Thanks! 

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