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%I #15 Jan 31 2021 20:40:26
%S 1,2,4,4,6,8,8,12,16,18,24,28,32,40,48,56,66,80,92,108,128,144,168,
%T 196,224,258,296,336,384,440,496,564,640,720,816,920,1030,1160,1304,
%U 1456,1632,1824,2032,2268,2528,2808,3120,3468,3840,4258,4716,5208,5760,6360
%N Coefficients of the eighth-order mock theta function V_0(q).
%H Vaclav Kotesovec, <a href="/A153176/b153176.txt">Table of n, a(n) for n = 0..10000</a>
%H B. Gordon and R. J. McIntosh, <a href="http://dx.doi.org/10.1112/S0024610700008735">Some eighth order mock theta functions</a>, J. London Math. Soc. 62 (2000), 321-335.
%F V_0(q) = -1 + 2*Sum_{n >= 0} q^(n^2)(1+q)(1+q^3)...(1+q^(2n-1))/((1-q)(1-q^3)...(1-q^(2n-1))).
%F a(n) ~ exp(Pi*sqrt(n)/2) / (2*sqrt(n)). - _Vaclav Kotesovec_, Jun 12 2019
%t nmax = 100; CoefficientList[Series[-1 + 2*Sum[x^(k^2) * Product[(1 + x^(2*j - 1))/(1 - x^(2*j - 1)), {j, 1, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 12 2019 *)
%o (PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = -1 + 2* sum(n = 0, nn, q^(n^2) * prod(k = 1, n, 1 + q^(2*k-1)) / prod(k = 1, n, 1 - q^(2*k-1))); Vec(gf) \\ _Michel Marcus_, Jun 18 2013
%Y Other '8th-order' mock theta functions are at A153148, A153149, A153155, A153156, A153172, A153174, A153178.
%K nonn
%O 0,2
%A _Jeremy Lovejoy_, Dec 20 2008
%E More terms from _Michel Marcus_, Feb 23 2015
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