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.

A306456 Expansion of Product_{j>=1} (1 - (-1 + Product_{k>=1} (1 - x^k))^j).

Original entry on oeis.org

1, 1, 0, -2, -1, -2, -3, -10, -15, -19, -17, 7, 59, 116, 102, -74, -468, -775, -242, 2111, 6388, 10102, 7421, -8768, -40024, -73196, -75164, -288, 182990, 445127, 639603, 478509, -380391, -2042730, -3922746, -4484102, -1857055, 4235012, 10177841, 8792321, -4085840
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 05 2019

Keywords

Crossrefs

Cf. A010815, A238440, A307127.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[(1 - (-1 + Product[(1 - x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[QPochhammer[QPochhammer[x] - 1], {x, 0, nmax}], x]

Formula

G.f.: g(g(x) - 1), where g(x) = g.f. of A010815.

A307569 Expansion of Product_{j>=1} (1 + x^j*Product_{k>=1} (1 + x^k)^j).

Original entry on oeis.org

1, 1, 2, 5, 13, 31, 77, 188, 458, 1113, 2693, 6494, 15614, 37441, 89563, 213771, 509166, 1210327, 2871563, 6800559, 16077631, 37948242, 89432015, 210456759, 494577391, 1160743593, 2720787358, 6369890095, 14895975508, 34795635421, 81192795264, 189262428612, 440739646423, 1025383979625
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 15 2019

Keywords

Crossrefs

Cf. A000009, A238440, A307128.

Programs

  • Mathematica
    nmax = 33; CoefficientList[Series[Product[(1 + x^j Product[(1 + x^k)^j, {k, 1, nmax}]), {j, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: g(x*g(x)), where g(x) = g.f. of A000009.

A307570 Expansion of Product_{j>=1} 1/(1 - x^j*Product_{k>=1} 1/(1 - x^k)^(k*j))^j.

Original entry on oeis.org

1, 1, 4, 15, 58, 215, 789, 2850, 10219, 36330, 128383, 450997, 1576384, 5484086, 18997492, 65547958, 225329592, 771920515, 2635815051, 8972752531, 30456389557, 103095375148, 348071445217, 1172252449310, 3938655968745, 13203699803684, 44167916497886, 147442143911193, 491220771388477
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 15 2019

Keywords

Crossrefs

Cf. A000219, A238440, A307321, A307571.

Programs

  • Mathematica
    nmax = 28; CoefficientList[Series[Product[1/(1 - x^j Product[1/(1 - x^k)^(k j), {k, 1, nmax}])^j, {j, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: g(x*g(x)), where g(x) = g.f. of A000219.
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.