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A368495 Psi-analog of the 5-core partition function. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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.
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
Sequence in context: A006703 A133623 A065862 * A189117 A365196 A372257
KEYWORD
sign,easy
AUTHOR
STATUS
approved

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Last modified May 18 11:53 EDT 2024. Contains 372630 sequences. (Running on oeis4.)