A368495 Psi-analog of the 5-core partition function.

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, 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, 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

Offset

0,4

Comments

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

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

Links

Table of n, a(n) for n=0..89.

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

Prog

(PARI)
q='q+O('q^99);
rpsi(q)=eta(q^2)^2 / eta(q);
gf=rpsi(-q^5)^5/rpsi(-q);
Vec(%) \\ Joerg Arndt, Dec 27 2023

Crossrefs

Cf. A053723, A368490.

Sequence in context: A006703 A133623 A065862 * A189117 A365196 A372257

Adjacent sequences: A368492 A368493 A368494 * A368496 A368497 A368498

Keyword

sign,easy

Author

Subhajit Bandyopadhyay, Dec 27 2023

Status

approved