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%I #32 Jan 31 2021 20:52:03
%S 1,-1,3,-5,6,-7,11,-16,18,-21,30,-40,47,-56,72,-92,108,-125,156,-193,
%T 225,-263,318,-383,444,-513,612,-724,834,-963,1129,-1320,1512,-1730,
%U 2010,-2325,2652,-3022,3474,-3988,4524,-5129,5857,-6673,7542,-8515,9660,-10943,12312,-13842
%N Coefficients of the '6th-order' mock theta function lambda(q).
%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 13
%H Vaclav Kotesovec, <a href="/A053272/b053272.txt">Table of n, a(n) for n = 0..1000</a> (corrected previous b-file from G. C. Greubel)
%H George E. Andrews and Dean Hickerson, <a href="https://doi.org/10.1016/0001-8708(91)90083-J">Ramanujan's "lost" notebook VII: The sixth order mock theta functions</a>, Advances in Mathematics, 89 (1991) 60-105.
%F G.f.: lambda(q) = Sum_{n >= 0} (-q)^n (1-q)(1-q^3)...(1-q^(2n-1))/((1+q)(1+q^2)...(1+q^n)).
%F a(n) ~ (-1)^n * exp(Pi*sqrt(n/3)) / (2*sqrt(3*n)). - _Vaclav Kotesovec_, Jun 15 2019
%t Series[Sum[(-q)^n Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+q^k, {k, 1, n}], {n, 0, 100}], {q, 0, 100}]
%t nmax = 100; CoefficientList[Series[Sum[(-x)^k * Product[1-x^j, {j, 1, 2*k-1, 2}] / Product[1+x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 15 2019 *)
%Y Other '6th-order' mock theta functions are at A053268, A053269, A053270, A053271, A053273, A053274.
%K sign,easy
%O 0,3
%A _Dean Hickerson_, Dec 19 1999
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