A294600 Expansion of 1/(Sum_{i>=0} q^(2*i*(i+1))/Product_{j=0..i} (1 + q^(2*j+1) + q^(4*j+2))).

1, 1, 1, 0, -1, -1, -1, 1, 2, 2, 1, -2, -4, -5, -2, 4, 9, 11, 4, -8, -20, -22, -7, 18, 42, 43, 12, -42, -89, -87, -19, 96, 189, 179, 28, -214, -399, -363, -32, 472, 838, 727, 6, -1041, -1760, -1452, 112, 2291, 3696, 2895, -487, -5015, -7735, -5740, 1551, 10929, 16135, 11298, -4377, -23741, -33587

Offset: 0

Author

Ilya Gutkovskiy, Nov 03 2017

Keywords

• sign

Comments

Convolution inverse of the 3rd order mock theta function rho(q) (A053255).

Links

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

Crossrefs

Cf. A053255, A294407, A294408, A294598, A294599.

Programs

Mathematica

nmax = 60; CoefficientList[Series[1/Sum[q^(2 i (i + 1))/Product[1 + q^(2 j + 1) + q^(4 j + 2), {j, 0, i}], {i, 0, nmax}], {q, 0, nmax}], q]

Formula

G.f.: 1/(Sum_{i>=0} q^(2*i*(i+1))/Product_{j=0..i} (1 + q^(2*j+1) + q^(4*j+2))).