A polynomial A_n(x;a) given by the associated Sheffer sequence with f(t) = t e^(a t), given by A_n(x;a) = x(x - a n)^(n - 1). The generating function is sum_(k = 0)^∞ (A_k(x;a))/(k!) t^k = e^(x W(a t)/a), where W(x) is the Lambert W-function. The associated binomial identity is (x + y)(x + y - a n)^(n - 1) = sum_(k = 0)^n(n k) x y(x - a k)^(k - 1) [y - a(n - k)]^(n - k - 1), where (n k) is a binomial coefficient, a formula originally due to Abel.
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