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A generalized Stirling inversion formula. (English) Zbl 1005.05003

Summary: We prove a simple functional identity from which a number of combinatorial identities of Stirling type can be easily deduced. The generalized Stirling inversion formula that we provide may be used to verify some well-known identities or find new ones, provided the generating functions are carefully chosen.

MSC:

05A10 Factorials, binomial coefficients, combinatorial functions
05A19 Combinatorial identities, bijective combinatorics
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