%I #20 Feb 16 2025 08:33:50

%S 1,-1,-1,1,1,-2,-1,4,0,-6,3,7,-8,-6,15,2,-24,9,33,-32,-35,68,20,-114,

%T 25,164,-120,-196,285,160,-521,16,796,-423,-1021,1166,999,-2310,-387,

%U 3774,-1296,-5194,4608,5735,-10007,-3870,17441,-2750,-25635,17116,31111

%N Expansion of 1 - x*(1+x)/(1 + x^2*(1-x^2)/(1 - x^3*(1+x^3)/(1 + x^4*(1-x^4)/(1 - x^5*(1+x^5)/(1 - ...))))), a continued fraction.

%H Seiichi Manyama, <a href="/A291200/b291200.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MockThetaFunction.html">Mock Theta Function</a>

%F a(n) = (-1)^n * A291193(n).

%F G.f.: 1/nu(-q) where nu(q) is the '3rd-order' mock theta function defined by Sum_{n >= 0} q^(n(n+1))/((1+q)(1+q^3)...(1+q^(2n+1))).

%F G.f.: 1/Sum_{n >= 0} q^(n(n+1))/((1-q)*(1-q^3)...(1-q^(2n+1)).

%Y Cf. A067357, A291193.

%K sign,changed

%O 0,6

%A _Seiichi Manyama_, Aug 20 2017