A294408 Expansion of 1/(1 + Sum_{i>=1} q^(i^2)/Product_{j=1..i} (1 + q^(2*j))).

1, -1, 1, 0, -2, 3, -2, -1, 6, -10, 8, 2, -19, 34, -30, -3, 60, -112, 106, -2, -188, 370, -373, 48, 586, -1226, 1307, -296, -1808, 4046, -4546, 1430, 5516, -13300, 15724, -6217, -16626, 43566, -54132, 25464, 49373, -142146, 185496, -100306, -143896, 461874, -632864, 384348, 409270, -1494356, 2150240

Offset: 0

Author

Ilya Gutkovskiy, Oct 30 2017

Keywords

• sign

Comments

Convolution inverse of the 3rd order mock theta function phi(q) (A053250).

Links

• Eric Weisstein's World of Mathematics, Mock Theta Function

Crossrefs

Cf. A053250, A081360, A294407.

Programs

Mathematica

nmax = 50; CoefficientList[Series[1/(1 + Sum[q^(i^2)/Product[1 + q^(2 j), {j, 1, i}], {i, 1, nmax}]), {q, 0, nmax}], q]

Formula

G.f.: 1/(1 + Sum_{i>=1} q^(i^2)/Product_{j=1..i} (1 + q^(2*j))).