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 1-4 of 4 results.

A321360 Expansion of Product_{1 <= i <= j <= k} 1/(1 - x^(i*j*k)).

Original entry on oeis.org

1, 1, 2, 3, 6, 8, 14, 19, 32, 44, 67, 91, 139, 186, 269, 362, 517, 686, 958, 1264, 1741, 2286, 3092, 4033, 5416, 7018, 9296, 11998, 15769, 20228, 26356, 33648, 43539, 55343, 71079, 89942, 114909, 144775, 183819, 230746, 291557, 364544, 458371, 571084, 714971, 887798, 1106704
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2018

Keywords

Links

Crossrefs

Cf. A034836, A174465, A182269, A321359, A321361.

Formula

Euler transform of A034836.
G.f.: Product_{k>0} 1/(1 - x^k)^A034836(k).

A321361 Expansion of Product_{1 <= i <= j <= k} (1 - x^(i*j*k)).

Original entry on oeis.org

1, -1, -1, 0, -1, 2, 0, 2, -1, 0, 3, -1, -2, -1, 1, -6, 0, -1, -1, 0, 6, 1, 1, 0, 4, 0, 0, 10, -2, -1, -9, 7, -11, 13, -15, -7, -3, -9, 0, 6, -3, -9, 14, -9, 20, -17, 20, -2, 20, 1, 25, -9, 14, 13, -3, -7, -21, -9, -11, 6, -54, 39, -22, -30, -10, 35, -21, 8, -41, -23
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2018

Keywords

Links

Crossrefs

Convolution inverse of A321360.
Cf. A034836, A319359, A321299, A321359.

Formula

G.f.: Product_{k>0} (1 - x^k)^A034836(k).

A321567 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} (1 + x^(i_1*i_2*i_3*i_4)).

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 6, 8, 11, 16, 21, 27, 38, 49, 63, 84, 109, 138, 180, 228, 289, 369, 463, 578, 732, 911, 1128, 1407, 1741, 2140, 2646, 3243, 3967, 4861, 5924, 7196, 8767, 10616, 12827, 15516, 18707, 22486, 27054, 32440, 38835, 46488, 55502, 66136, 78836, 93727, 111265
Offset: 0

Views

Author

Seiichi Manyama, Nov 13 2018

Keywords

Links

Crossrefs

Product_{1 <= i_1 <= i_2 <= ... <= i_b} (1 + x^(i_1 * i_2 * ... * i_b)): A000009 (b=1), A211856 (b=2), A321359 (b=3), this sequence (b=4).
Cf. A066806, A218320, A321566.

Formula

G.f.: Product_{k>0} (1 + x^k)^A218320(k).

A321374 Expansion of Product_{1 < i <= j <= k} (1 + x^(i*j*k)).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 1, 3, 0, 2, 0, 5, 0, 1, 1, 8, 0, 3, 1, 8, 0, 5, 1, 12, 2, 4, 2, 18, 0, 9, 3, 18, 2, 14, 3, 28, 3, 13, 5, 39, 2, 22, 10, 42, 5, 32, 8, 61, 8, 34, 14, 85, 7, 52, 22, 91, 14, 74, 20, 132, 24, 80
Offset: 0

Views

Author

Seiichi Manyama, Nov 08 2018

Keywords

Links

Crossrefs

Cf. A122179, A211857, A321359.

Formula

G.f.: Product_{k>0} (1 + x^k)^A122179(k).
Showing 1-4 of 4 results.

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

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