Polynomials s_k(x;λ, μ) which are a generalization of the Boole polynomials, form the Sheffer sequence for g(t) | = | (1 + e^(λ t))^μ f(t) | = | e^t - 1 and have generating function sum_(k = 0)^∞ (s_k(x;λ, μ))/(k!) t^k = [1 + (1 + t)^λ]^(-μ) (1 + t)^x. The first few are s_0(x;λ, μ) | = | 2^(-μ) s_1(x;λ, μ) | = | 2^(-(μ + 1))(2x - λμ) and s_2(x;λ, μ) = 2^(-(μ + 2))[4x(x - 1) + (2 - 4x) λμ + μ(μ - 1) λ^2].