Acknowledgement
The author is grateful to the anonymous referee for the valuable suggestions. In particular, the referee notices a connection between the generating function for p2k,k(n) in Andrews and Newman [3] and the generating function for ck(n).
References
- Z. Ahmed, N. D. Baruah, and M. G. Dastidar, New congruences modulo 5 for the number of 2-color partitions, J. Number Theory 157 (2015), 184-198. https://doi.org/10.1016/j.jnt.2015.05.002
- G. E. Andrews, The Theory of Partitions, reprint of the 1976 original, Cambridge Mathematical Library, Cambridge Univ. Press, Cambridge, 1998.
- G. E. Andrews and D. Newman, The minimal excludant in integer partitions, J. Integer Seq. 23 (2020), no. 2, Paper No. 20.2.3, 11 pp.
- B. C. Berndt, Number Theory in the Spirit of Ramanujan, Student Mathematical Library, 34, Amer. Math. Soc., Providence, RI, 2006. https://doi.org/10.1090/stml/034
- Z. Cao, On Somos' dissection identities, J. Math. Anal. Appl. 365 (2010), no. 2, 659-667. https://doi.org/10.1016/j.jmaa.2009.11.038
- Z. Cao, Integer matrix exact covering systems and product identities for theta functions, Int. Math. Res. Not. IMRN 2011 (2011), no. 19, 4471-4514. https://doi.org/10.1093/imrn/rnq253
- H.-C. Chan, Ramanujan's cubic continued fraction and an analog of his "most beautiful identity", Int. J. Number Theory 6 (2010), no. 3, 673-680. https://doi.org/10.1142/S1793042110003150
- G. Gasper and M. Rahman, Basic Hypergeometric Series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge Univ. Press, Cambridge, 2004. https://doi.org/10.1017/CBO9780511526251
- J. Huh and B. Kim, The number of equivalence classes arising from partition involutions, Int. J. Number Theory 16 (2020), no. 5, 925-939. https://doi.org/10.1142/S1793042120500475
- M. Merca, A further look at cubic partitions, Ramanujan J. 59 (2022), no. 1, 253-277. https://doi.org/10.1007/s11139-021-00522-8
- S. O. Warnaar, Partial theta functions, Ramanujan Encyclopedia, to appear.