cp's OEIS Frontend

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

%I A373535 #12 Sep 13 2024 07:42:04
%S A373535 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 A373535 10,11,9,8,10,12,11,16,14,12,17,13,13,17,13,17,18,18,17,17,15,18,19,
%U A373535 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 A373535 Number of self-conjugate 10 core partitions of n.
%C A373535 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 A373535 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 A373535 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 A373535 (PARI)
%o A373535 q='q+O('q^80);
%o A373535 chi(q) = eta(q^2)^2 / (eta(q)*eta(q^4));
%o A373535 gf = chi(q) * eta(q^20)^5;
%o A373535 Vec(%)
%Y A373535 Cf. A182805.
%K A373535 easy,nonn
%O A373535 0,9
%A A373535 _Subhajit Bandyopadhyay_, Aug 23 2024