%I #16 Jan 31 2021 20:39:37

%S 1,-1,2,-2,3,-4,5,-6,8,-9,11,-14,17,-20,24,-28,33,-39,46,-53,62,-72,

%T 83,-96,110,-126,145,-165,188,-214,243,-275,312,-352,396,-447,502,

%U -563,632,-707,791,-884,986,-1098,1223,-1359,1509,-1676,1857,-2056,2276,-2515

%N Coefficients of the eighth-order mock theta function T_1(q).

%H Vaclav Kotesovec, <a href="/A153156/b153156.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 G.f.: Sum{n >= 0} q^(n^2+n) (1+q^2)(1+q^4)...(1+q^(2n))/(1+q)(1+q^3)...(1+q^(2n+1)).

%F a(n) ~ (-1)^n * sqrt(1 + sqrt(2)) * exp(Pi*sqrt(n)/2) / (2^(11/4) * sqrt(n)). - _Vaclav Kotesovec_, Jun 14 2019

%t nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)) * Product[(1 + x^(2*j)), {j, 1, k}] / Product[(1 + x^(2*j+1)), {j, 0, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 13 2019 *)

%o (PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^(n^2+n) * prod(k = 1, n, 1 + q^(2*k)) / prod(k = 0, 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, A153172, A153174, A153176, A153178.

%K sign

%O 0,3

%A _Jeremy Lovejoy_, Dec 19 2008

%E More terms from _Michel Marcus_, Feb 23 2015