%I #15 Jan 31 2021 20:40:40
%S 0,1,1,1,2,3,3,4,5,6,8,9,11,14,16,19,23,27,31,37,43,49,58,66,76,89,
%T 101,115,132,150,170,194,219,247,280,315,354,399,447,500,562,627,699,
%U 781,869,967,1076,1194,1323,1468,1625,1796,1987,2193,2418,2668,2937,3231
%N Coefficients of the eighth-order mock theta function V_1(q).
%H Vaclav Kotesovec, <a href="/A153178/b153178.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_1(q) = Sum_{n >= 0} q^((n+1)^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^(5/2) * sqrt(n)). - _Vaclav Kotesovec_, Jun 12 2019
%t nmax = 100; CoefficientList[Series[Sum[x^((k+1)^2) * Product[(1 + x^(2*j - 1)), {j, 1, k}] / Product[(1 - x^(2*j - 1)), {j, 1, k+1}], {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 = sum(n = 0, nn, q^((n+1)^2) * prod(k = 1, n, 1 + q^(2*k-1)) / prod(k = 0, n, 1 - q^(2*k+1))); for (i=0, nn-1, print1(polcoeff(gf, i), ", "););} \\ _Michel Marcus_, Jun 18 2013
%Y Other '8th-order' mock theta functions are at A153148, A153149, A153155, A153156, A153172, A153174, A153176.
%K nonn
%O 0,5
%A _Jeremy Lovejoy_, Dec 20 2008
%E More terms from _Michel Marcus_, Feb 23 2015