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%I #8 Nov 07 2017 03:02:22
%S 1,-1,3,-8,20,-51,132,-339,868,-2228,5720,-14676,37659,-96644,248004,
%T -636413,1633144,-4190920,10754580,-27598012,70821032,-181738372,
%U 466370429,-1196782952,3071141180,-7881051500,20224069573,-51898276576,133179482008,-341760374284,877013123076,-2250559385788
%N Expansion of 1/(1 + Sum_{i>=1} q^(i^2)/Product_{j=1..i} (1 + q^j)^2).
%C Convolution inverse of the 3rd order mock theta function f(q) (A000025).
%H Robert Israel, <a href="/A294407/b294407.txt">Table of n, a(n) for n = 0..2441</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MockThetaFunction.html">Mock Theta Function</a>
%F G.f.: 1/(1 + Sum_{i>=1} q^(i^2)/Product_{j=1..i} (1 + q^j)^2).
%p N:= 50: # to get a(0)..a(N)
%p g:= 1/(1+add(q^(i^2)/mul(1+q^j,j=1..i)^2, i=1..floor(sqrt(N)))):
%p S:= series(g, q, N+1):
%p seq(coeff(S,q,n),n=0..N); # _Robert Israel_, Nov 06 2017
%t nmax = 31; CoefficientList[Series[1/(1 + Sum[q^(i^2)/Product[(1 + q^j)^2, {j, 1, i}], {i, 1, nmax}]), {q, 0, nmax}], q]
%Y Cf. A000025, A000039, A000199, A010815.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Oct 30 2017
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