Short-wavelength single-pass free electron lasers (FEL) are capable of generating transverse-coherent and high-power radiations. Compared with the self-amplified spontaneous emission (SASE) FEL scheme, seeded FEL schemes can, in principle, improve the longitudinal coherence of radiation pulses. In recent years, the research community has pursued the realization of high-repetition-rate (MHz) and high-average-power (kW) seeded FELs. To alleviate the requirements of external seeding lasers, many novel seeding schemes have been proposed, which are currently limited by the state-of-the-art laser systems. An analytical study of a recently proposed seeding scheme based on direct-amplification-enabled harmonic generation (DEHG) is presented herein. In contrast to the complete numerical simulations and optimization design, this study starts from one-dimensional FEL equations of motion and derives an analytical formula for the harmonic bunching factor at the chicane exit after the electron beam traverses the modulator undulator. Additionally, to obtain a quick estimate of downstream high-gain FEL performance, we constructed a linear high-gain FEL transport matrix, including the three-dimensional effects incorporated by the Ming-Xie formula. As an application of the analytical formulas, we discuss three different cases for designing and optimizing the seeding scheme. We expect this analytical approach to shed light on seeding designs that aim to produce the desired high-brightness mirobunched electron beam.