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%I #30 Jan 31 2021 20:51:33
%S 1,-1,2,-1,1,-3,3,-3,4,-4,6,-6,5,-9,11,-10,11,-15,17,-16,19,-22,26,
%T -29,29,-36,42,-42,46,-55,60,-64,71,-79,90,-95,101,-117,131,-137,148,
%U -169,184,-195,211,-234,258,-276,295,-327,360,-379,409,-453,489,-522,563,-612,666,-710,757,-829,898
%N Coefficients of the '6th-order' mock theta function phi(q).
%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 2, 4, 6, 13, 16, 17
%H Vaclav Kotesovec, <a href="/A053268/b053268.txt">Table of n, a(n) for n = 0..10000</a> (corrected and extended 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.: phi(q) = sum for n >= 0 of (-1)^n q^n^2 (1-q)(1-q^3)...(1-q^(2n-1))/((1+q)(1+q^2)...(1+q^(2n))).
%F a(n) ~ (-1)^n * exp(Pi*sqrt(n/6)) / (2*sqrt(3*n)). - _Vaclav Kotesovec_, Jun 15 2019
%t Series[Sum[(-1)^n q^n^2 Product[1-q^k, {k, 1, 2n-1, 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-1, 2}] / Product[1+x^j, {j, 1, 2*k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 15 2019 *)
%Y Other '6th-order' mock theta functions are at A053269, A053270, A053271, A053272, A053273, A053274.
%K sign,easy
%O 0,3
%A _Dean Hickerson_, Dec 19 1999
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