A321360 -id:A321360 - cp's OEIS frontend

A321359 Expansion of Product_{1 <= i <= j <= k} (1 + x^(ijk)).

1, 1, 1, 2, 3, 4, 6, 8, 11, 16, 21, 27, 38, 49, 63, 84, 108, 137, 179, 226, 286, 365, 457, 570, 720, 894, 1106, 1378, 1700, 2087, 2577, 3151, 3847, 4707, 5723, 6941, 8439, 10197, 12300, 14852, 17863, 21433, 25740, 30797, 36794, 43963, 52372, 62288, 74098, 87905, 104149

Offset: 0

Seiichi Manyama, Nov 07 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A034836, A211856, A280473, A321360, A321361.

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

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

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

Seiichi Manyama, Nov 07 2018

sign

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Convolution inverse of A321360.

Cf. A034836, A319359, A321299, A321359.

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

A321566 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} 1/(1 - x^(i_1i_2i_3*i_4)).

Original entry on oeis.org

1, 1, 2, 3, 6, 8, 14, 19, 32, 44, 67, 91, 139, 186, 269, 362, 518, 687, 960, 1267, 1747, 2294, 3106, 4052, 5449, 7063, 9365, 12092, 15914, 20422, 26639, 34029, 44090, 56075, 72108, 91303, 116802, 147264, 187210, 235182, 297562, 372346, 468777, 584553, 732803, 910744

Offset: 0

Seiichi Manyama, Nov 13 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Transforms

Product_{1 <= i_1 <= i_2 <= ... <= i_b} 1/(1 - x^(i_1 * i_2 * ... * i_b)): A000041 (b=1), A182269 (b=2), A321360 (b=3), this sequence (b=4).

Cf. A066739, A218320, A321567.

Euler transform of A218320.

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

A321375 Expansion of Product_{1 < i <= j <= k} 1/(1 - x^(ijk)).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 5, 0, 1, 1, 4, 0, 2, 0, 9, 0, 2, 1, 12, 0, 3, 1, 16, 0, 7, 2, 20, 2, 6, 2, 36, 0, 13, 5, 37, 2, 21, 4, 60, 3, 23, 9, 80, 4, 35, 14, 106, 5, 58, 16, 137, 12, 66, 22, 210, 10, 100, 40, 238, 22, 147

Offset: 0

Seiichi Manyama, Nov 08 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Transforms

Cf. A122179, A182270, A321360.

Euler transform of A122179.

G.f.: Product_{k>0} 1/(1 - x^k)^A122179(k).

cp's OEIS Frontend

A321359 Expansion of Product_{1 <= i <= j <= k} (1 + x^(ijk)).

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

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A321566 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} 1/(1 - x^(i_1i_2i_3*i_4)).

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A321375 Expansion of Product_{1 < i <= j <= k} 1/(1 - x^(ijk)).

Views

Author

Keywords

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Formula

cp's OEIS Frontend

A321359 Expansion of Product_{1 <= i <= j <= k} (1 + x^(i*j*k)).

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

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Formula

A321566 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} 1/(1 - x^(i_1*i_2*i_3*i_4)).

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A321375 Expansion of Product_{1 < i <= j <= k} 1/(1 - x^(i*j*k)).

Views

Author

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Links

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Formula

A321359 Expansion of Product_{1 <= i <= j <= k} (1 + x^(ijk)).

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

A321566 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} 1/(1 - x^(i_1i_2i_3*i_4)).

A321375 Expansion of Product_{1 < i <= j <= k} 1/(1 - x^(ijk)).