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Number of self-conjugate 10 core partitions of n.
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%I #12 Sep 13 2024 07:42:04

%S 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,

%T 10,11,9,8,10,12,11,16,14,12,17,13,13,17,13,17,18,18,17,17,15,18,19,

%U 17,18,18,17,24,28,16,25,26,24,22,25,26,25,28,22,31,31,25,33,39,32,31,37

%N Number of self-conjugate 10 core partitions of n.

%C 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).

%H Frank Garvan, Dongsu Kim, and Dennis Stanton, <a href="https://doi.org/10.1007/BF01231493">Cranks and t-cores</a>, Invent. Math. 101 (1990):1-17.

%F 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).

%o (PARI)

%o q='q+O('q^80);

%o chi(q) = eta(q^2)^2 / (eta(q)*eta(q^4));

%o gf = chi(q) * eta(q^20)^5;

%o Vec(%)

%Y Cf. A182805.

%K easy,nonn

%O 0,9

%A _Subhajit Bandyopadhyay_, Aug 23 2024