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Congruence and Recurrence Properties of Lehmer-Euler Numbers

A number-theoretic study of Lehmer's generalized Euler numbers W_n (nonzero only when 3 divides n), establishing new congruences modulo primes and prime powers together with recurrence, explicit-summation, and Toeplitz-Hessenberg determinant (Trudi-formula) expressions and an inversion relation, introducing an associated polynomial sequence with its properties, and deriving identities that connect the numbers to the classical Euler numbers and to central factorial numbers.