OFFSET
0,2
COMMENTS
a_t(n), the phi-analog of the t-core partition function, is defined in the article by Gireesh, Ray and Shivashankar (2021). This sequence is for a_5(n).
LINKS
S. Bandyopadhyay and N. D. Baruah, Arithmetic Identities for Some Analogs of the 5-Core Partition Function, Journal of Integer Sequences, 27 (2024): Article 24.4.5.
Subhajit Bandyopadhyay and Nayandeep Deka Baruah, Arithmetic Identities for Some Analogs of 5-core Partition Function, arXiv:2409.02034 [math.NT], 2024.
D. S. Gireesh, C. Ray, and C. Shivashankar, A new analogue of t-core partitions, Acta Arithmetica, 199 (2021):33-53.
FORMULA
G.f.: phi(-q^5)^5/phi(-q), where phi(q) is the Ramanujan's theta function phi (see A000122).
PROG
(PARI)
q='q+O('q^71);
phi(q)=eta(q^2)^5 / (eta(q)*eta(q^4))^2;
gf=phi(-q^5)^5/phi(-q);
Vec(%) \\ Joerg Arndt, Dec 27 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Subhajit Bandyopadhyay, Dec 27 2023
STATUS
approved