A153149 - OEIS

%I #16 Jan 31 2021 20:39:02

%S 1,0,0,1,1,-1,-1,1,2,0,-2,1,2,-2,-2,2,3,-1,-2,2,2,-3,-4,3,5,-2,-4,3,5,

%T -4,-6,4,7,-4,-7,5,7,-6,-9,7,11,-6,-10,7,11,-9,-14,9,15,-9,-14,11,16,

%U -13,-19,13,21,-12,-22,15,23,-18,-26,19,30,-19,-30,21,31

%N Coefficients of the eighth-order mock theta function S_1(q).

%H Seiichi Manyama, <a href="/A153149/b153149.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+2n) (1+q)(1+q^3)...(1+q^(2n-1))/(1+q^2)(1+q^4)...(1+q^(2n)).

%o (PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^(n^2+2*n) * prod(k = 1, n, 1 + q^(2*k-1)) / prod(k = 1, n, 1 + q^(2*k))); Vec(gf) \\ _Michel Marcus_, Jun 18 2013

%Y Other '8th-order' mock theta functions are at A153148, A153155, A153156, A153172, A153174, A153176, A153178.

%K sign

%O 0,9

%A _Jeremy Lovejoy_, Dec 19 2008

%E More terms from _Michel Marcus_, Feb 23 2015