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A373535
Number of self-conjugate 10 core partitions of n.
0
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
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved