The deployment of large language models (LLMs) in healthcare has demonstrated substantial potential for enhancing clinical decision-making, administrative efficiency, and patient outcomes. However, the underrepresentation of diverse groups in the development and application of these models can perpetuate biases, leading to inequitable healthcare delivery. This paper presents a comprehensive scientometric analysis of LLM research for healthcare, including data from January 1, 2021, to June 16, 2024. By analyzing metadata from PubMed and Dimensions, including author affiliations, countries, and funding sources, we assess the diversity of contributors to LLM research. Our findings highlight significant gender and geographic disparities, with a predominance of male authors and contributions primarily from high-income countries (HICs). We introduce a novel journal diversity index based on Gini impurity to measure the inclusiveness of scientific publications. Our results underscore the necessity for greater representation in order to ensure the equitable application of LLMs in healthcare. We propose actionable strategies to enhance diversity and inclusivity in artificial intelligence research, with the ultimate goal of fostering a more inclusive and equitable future in healthcare innovation.