A polynomial given by the associated Sheffer sequence with
(1)
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given by
(2)
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The generating function is
(3)
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where is the Lambert W-function. The associated binomial identity is
(4)
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where is a binomial coefficient, a formula originally due to Abel (Riordan 1979, p. 18; Roman 1984, pp. 30 and 73).
The first few Abel polynomials are
(5)
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(6)
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(7)
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(8)
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(9)
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