cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A294598 Expansion of 1/(Sum_{i>=0} q^(i^2)/Product_{j=1..i} (1 - q^j + q^(2*j))).

Original entry on oeis.org

1, -1, 0, 1, -1, 0, 0, 0, 1, -2, 2, 0, -3, 4, -3, 1, 1, -4, 9, -10, 2, 11, -19, 16, -7, -5, 22, -40, 43, -13, -42, 86, -87, 44, 24, -106, 183, -195, 74, 163, -382, 430, -256, -86, 504, -859, 907, -395, -639, 1697, -2084, 1399, 236, -2313, 4037, -4301, 2080, 2529, -7561, 9923, -7327
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 03 2017

Keywords

Comments

Convolution inverse of the 3rd order mock theta function chi(q) (A053252).

Links

Crossrefs

Cf. A053252, A294407, A294408, A294599, A294600.

Programs

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

Formula

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

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

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Nov 03 2017

Keywords

Comments

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

Links

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))).

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))).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Nov 03 2017

Keywords

Comments

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

Links

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))).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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