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%I #27 Jun 12 2019 03:10:16
%S 1,-1,1,0,1,-2,1,-1,1,-2,3,-1,2,-4,3,-2,3,-5,4,-4,5,-6,7,-5,6,-9,9,-7,
%T 9,-12,11,-11,12,-15,16,-14,16,-21,20,-18,22,-25,26,-25,28,-33,34,-33,
%U 35,-42,43,-41,47,-53,53,-54,57,-65,69,-67,73,-83,85,-83,92,-102,104,-106,114,-125,130,-130,139,-154
%N Coefficients of the '10th-order' mock theta function X(q).
%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9
%H Vaclav Kotesovec, <a href="/A053283/b053283.txt">Table of n, a(n) for n = 0..10000</a> (corrected and extended previous b-file from G. C. Greubel)
%H Youn-Seo Choi, <a href="http://dx.doi.org/10.1007/s002220050318">Tenth order mock theta functions in Ramanujan's lost notebook</a>, Inventiones Mathematicae, 136 (1999) p. 497-569.
%F G.f.: X(q) = Sum_{n >= 0} (-1)^n q^n^2/((1+q)(1+q^2)...(1+q^(2n))).
%F a(n) ~ (-1)^n * exp(Pi*sqrt(n/10)) / (2*5^(1/4)*sqrt(phi*n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jun 12 2019
%t Series[Sum[(-1)^n q^n^2/Product[1+q^k, {k, 1, 2n}], {n, 0, 10}], {q, 0, 100}]
%t nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^(k^2) / Product[1+x^j, {j, 1, 2*k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 11 2019 *)
%Y Other '10th-order' mock theta functions are at A053281, A053282, A053284.
%K sign,easy
%O 0,6
%A _Dean Hickerson_, Dec 19 1999
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