A321361 -id:A321361 - 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).

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

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

Seiichi Manyama, Nov 07 2018

nonn

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

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

Euler transform of A034836.

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

A321376 Expansion of Product_{1 < i <= j <= k} (1 - x^(ijk)).

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, 0, 0, 0, 0, -1, 0, 1, -1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 2, 0, 1, 1, 4, 0, 0, 0, 2, 0, -1, 1, 2, 0, 0, -1, 2, 1, -1, -1, -1, 0, -2, 0, -4, -1, 2, -2, -3, 0, -4, -4, -1, -1, -6, -2, -7, 0, 2, -2, -10

Offset: 0

Seiichi Manyama, Nov 08 2018

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

Cf. A122179, A321361, A321374, A321375, A321377.

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

A319517 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} (1 - x^(i_1i_2i_3*i_4)).

Original entry on oeis.org

1, -1, -1, 0, -1, 2, 0, 2, -1, 0, 3, -1, -2, -1, 1, -6, -1, 0, 0, 0, 7, -1, 1, -2, 4, 1, -2, 11, 1, -2, -10, 11, -11, 15, -16, -6, -7, -10, -1, 10, -5, -10, 12, -20, 19, -16, 24, -2, 28, -9, 41, -6, 15, 20, 4, -21, -15, -13, -14, 13, -73, 67, -30, -44, -19, 31, -30

Offset: 0

Seiichi Manyama, Nov 14 2018

sign

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

Convolution inverse of A321566.
Product_{1 <= i_1 <= i_2 <= ... <= i_b} (1 - x^(i_1 * i_2 * ... * i_b)): A010815 (b=1), A321299 (b=2), A321361 (b=3), this sequence (b=4).
Cf. A218320, A321460, A321567.

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

cp's OEIS Frontend

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

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

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A321376 Expansion of Product_{1 < i <= j <= k} (1 - x^(ijk)).

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A319517 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} (1 - x^(i_1i_2i_3*i_4)).

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cp's OEIS Frontend

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

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

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Author

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Formula

A321376 Expansion of Product_{1 < i <= j <= k} (1 - x^(i*j*k)).

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A319517 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} (1 - x^(i_1*i_2*i_3*i_4)).

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

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

A321376 Expansion of Product_{1 < i <= j <= k} (1 - x^(ijk)).

A319517 Expansion of Product_{1 <= i_1 <= i_2 <= i_3 <= i_4} (1 - x^(i_1i_2i_3*i_4)).