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From Michael Somos, Apr 25 2003: (Start)
Expansion of q^(-1) * eta(q^2)^2 * eta(q^5) * eta(q^20) / (eta(q) * eta(q^4)) in powers of q. - _Michael Somos_, Apr 25 2003
Euler transform of period 20 sequence [1, -1, 1, 0, 0, -1, 1, 0, 1, -2, 1, 0, 1, -1, 0, 0, 1, -1, 1, -2, ...]. - _Michael Somos_, Apr 25 2003
G.f.: Product_{k>0} (1 - x^(10*k))^2 * (1 + x^(2*k - 1)) / (1 + x^(10*k - 5)). - _Michael Somos_, Apr 25 2003(End)
F. Frank Garvan, D. Dongsu Kim , and D. Dennis Stanton, <a href="http://dx.doi.org/10.1007/BF01231493">Cranks and t-cores</a>, Invent. Math. 101 (1990), no. 1, 1-17.
Christopher R. H. Hanusa and Rishi Nath, <a href="httphttps://arxiv.org/abs/1201.6629">The number of self-conjugate core partitions</a>, arxiv:1201.6629 [math.NT], 2012. See Table 1 , p. 15.
B. Bruce C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, 1991, see p. 258 , Entry 9(iii).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/5. - Amiram Eldar, Jan 27 2024
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