Recent Multi-Party Conversation (MPC) models typically rely on graph-based approaches to capture dialogue structures. However, these methods have limitations, such as information loss during the projection of utterances into structural embeddings and constraints in leveraging pre-trained language models directly. In this paper, we propose \textbf{SS-MPC}, a response generation model for MPC that eliminates the need for explicit graph structures. Unlike existing models that depend on graphs to analyze conversation structures, SS-MPC internally encodes the dialogue structure as a sequential input, enabling direct utilization of pre-trained language models. Experimental results show that \textbf{SS-MPC} achieves \textbf{15.60\% BLEU-1} and \textbf{12.44\% ROUGE-L} score, outperforming the current state-of-the-art MPC response generation model by \textbf{3.91\%p} in \textbf{BLEU-1} and \textbf{0.62\%p} in \textbf{ROUGE-L}. Additionally, human evaluation confirms that SS-MPC generates more fluent and accurate responses compared to existing MPC models.