Is the Sibuya distribution a progeny?

Gérard Letac. Is the Sibuya distribution a progeny?. J. Applied Probability, 56(1):52-56, 2019. [doi]

@article{Letac19,
  title = {Is the Sibuya distribution a progeny?},
  author = {Gérard Letac},
  year = {2019},
  doi = {10.1017/jpr.2019.5},
  url = {https://doi.org/10.1017/jpr.2019.5},
  researchr = {https://researchr.org/publication/Letac19},
  cites = {0},
  citedby = {0},
  journal = {J. Applied Probability},
  volume = {56},
  number = {1},
  pages = {52-56},
}