A368495 - OEIS

%I #20 Sep 04 2024 08:48:23

%S 1,1,1,2,3,-1,0,2,0,-2,6,6,3,5,8,0,0,1,0,0,11,6,6,12,10,-6,0,6,0,-5,

%T 12,16,9,7,18,0,0,3,0,0,21,12,7,22,23,-6,0,12,0,-12,26,20,12,18,20,0,

%U 0,-2,0,0,21,21,18,24,33,-16,0,18,0,-7,36,36,13,20,36,0,0,9,0,0,41,12,24,42,30,-12,0,14,0,-22

%N Psi-analog of the 5-core partition function.

%C a(n) is a natural analog to A368490 and the 5-core partition function (see A053723). They have similar generating functions.

%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122) and psi(q) (A010054)

%H S. Bandyopadhyay and N. D. Baruah, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Baruah/bar6.html">Arithmetic Identities for Some Analogs of the 5-Core Partition Function</a>, Journal of Integer Sequences, 27 (2024): Article 24.4.5.

%H Subhajit Bandyopadhyay and Nayandeep Deka Baruah, <a href="https://arxiv.org/abs/2409.02034">Arithmetic Identities for Some Analogs of 5-core Partition Function</a>, arXiv:2409.02034 [math.NT], 2024.

%H D. S. Gireesh, C. Ray, and C. Shivashankar, <a href="https://dx.doi.org/10.4064/aa200516-10-12">A new analogue of t-core partitions</a>, Acta Arithmetica, 199 (2021):33-53.

%F G.f.: psi(-q^5)^5/psi(-q), where psi(q) is the Ramanujan's theta function psi (see A010054)

%o (PARI)

%o q='q+O('q^99);

%o rpsi(q)=eta(q^2)^2 / eta(q);

%o gf=rpsi(-q^5)^5/rpsi(-q);

%o Vec(%) \\ _Joerg Arndt_, Dec 27 2023

%Y Cf. A053723, A368490.

%K sign,easy

%O 0,4

%A _Subhajit Bandyopadhyay_, Dec 27 2023