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

0,9

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

Table of n, a(n) for n=0..79.

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

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).

Prog

(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(%)

Crossrefs

Cf. A182805.

Sequence in context: A169991 A035435 A169992 * A025775 A169993 A325620

Adjacent sequences: A373532 A373533 A373534 * A373536 A373537 A373538

Keyword

easy,nonn,new

Author

Subhajit Bandyopadhyay, Aug 23 2024

Status

approved