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%I #34 Jan 31 2021 20:45:52
%S 1,1,0,1,1,1,0,2,1,2,1,2,1,3,2,3,3,3,2,5,3,5,4,6,5,7,5,7,7,9,7,11,9,
%T 11,11,13,12,15,13,17,16,19,17,23,21,24,23,27,26,32,29,34,34,38,37,44,
%U 42,48,48,54,52,60,58,66,67,73,72,82,81,90,90,100,99,111,110,121,123
%N Coefficients of the '7th-order' mock theta function F_0(q).
%C The rank of a partition is its largest part minus the number of parts.
%D Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355.
%D Atle Selberg, Uber die Mock-Thetafunktionen siebenter Ordnung, Arch. Math. Naturvidenskab, 41 (1938) 3-15.
%H Terry Thibault, Frank Garvan, <a href="/A053275/b053275.txt">Table of n, a(n) for n = 0..10000</a> (terms up to n = 1000 by G. C. Greubel)
%H George E. Andrews, <a href="http://dx.doi.org/10.1090/S0002-9947-1986-0814916-2">The fifth and seventh order mock theta functions</a>, Trans. Amer. Math. Soc., 293 (1986) 113-134.
%H Dean Hickerson, <a href="https://doi.org/10.1007/BF01394280">On the seventh order mock theta functions</a>, Inventiones Mathematicae, 94 (1988) 661-677.
%F G.f.: F_0(q) = Sum_{n >= 0} q^n^2/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n))).
%F a(n) = number of partitions of 7n with rank == 0 (mod 7) minus number with rank == 2 (mod 7).
%F a(n) ~ sin(Pi/7) * exp(Pi*sqrt(2*n/21)) / sqrt(7*n/2). - _Vaclav Kotesovec_, Jun 15 2019
%t Series[Sum[q^n^2/Product[1-q^k, {k, n+1, 2n}], {n, 0, 10}], {q, 0, 100}]
%t nmax = 100; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^j, {j, k+1, 2*k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 14 2019 *)
%Y Other '7th-order' mock theta functions are at A053276, A053277, A053278, A053279, A053280.
%K nonn,easy
%O 0,8
%A _Dean Hickerson_, Dec 19 1999
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