I assume that with ‘one-to-many’, you mean to have one single input that is mapped to outputs at multiple time steps. The best approach would probably depend on your actual problem, but one way would be to have an initial trainable input vector that is simply fed as input for every single time step.
Before I get into too many details here, I would actually recommend this 36 well written SO answer that explains the implementation details very well, for Keras though