A294599 Expansion of 1/(Sum_{i>=0} q^(2*i*(i+1))/Product_{j=0..i} (1 - q^(2*j+1))^2).

1, -2, 1, 0, -1, 2, -1, -2, 5, -4, -2, 10, -13, 4, 16, -32, 24, 14, -62, 76, -17, -100, 185, -126, -108, 382, -426, 36, 655, -1098, 650, 798, -2352, 2402, 115, -4186, 6441, -3234, -5612, 14296, -13307, -2750, 26556, -37524, 15220, 38448, -86366, 72836, 28545, -166734, 216788, -65702, -257380

Offset: 0

Author

Ilya Gutkovskiy, Nov 03 2017

Keywords

• sign

Comments

Convolution inverse of the 3rd-order mock theta function omega(q) (A053253).

Links

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

Crossrefs

Cf. A053253, A294407, A294408, A294598, A294600.

Programs

Mathematica

nmax = 52; CoefficientList[Series[1/Sum[q^(2 i (i + 1))/Product[(1 - q^(2 j + 1))^2, {j, 0, i}], {i, 0, nmax}], {q, 0, nmax}], q]
nmax = 52; CoefficientList[Series[1/Sum[q^i/Product[1 - q^(2 j + 1), {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))^2).

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