A373535 Number of self-conjugate 10 core partitions of n.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 2, 3, 8, 4, 6, 7, 7, 9, 6, 7, 8, 10, 8, 10, 11, 9, 8, 10, 12, 11, 16, 14, 12, 17, 13, 13, 17, 13, 17, 18, 18, 17, 17, 15, 18, 19, 17, 18, 18, 17, 24, 28, 16, 25, 26, 24, 22, 25, 26, 25, 28, 22, 31, 31, 25, 33, 39, 32, 31, 37

Offset: 0

Author

Subhajit Bandyopadhyay, Aug 23 2024

Keywords

• easy
• nonn

Comments

The generating function for sc_t(n), the number of t-core partitions of n, is given in Section 7 of the article titled 'Cranks and t-cores' by Garvan, Kim, and Stanton (1990). This sequence is sc_10(n).

Links

• Frank Garvan, Dongsu Kim, and Dennis Stanton, Cranks and t-cores, Invent. Math. 101 (1990):1-17.

Crossrefs

Cf. A182805.

Programs

PARI

q='q+O('q^80);
chi(q) = eta(q^2)^2 / (eta(q)*eta(q^4));
gf = chi(q) * eta(q^20)^5;
Vec(%)

Formula

G.f.: chi(q) * f(-q^20)^5, where chi(q) is Ramanujan's chi function (see A000700) and f(q) is Ramanujan's theta function f(q) (see A121373).