A327064 -id:A327064 - cp's OEIS frontend

A327063 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^j).

1, 1, 1, 2, 4, 5, 8, 11, 15, 24, 34, 43, 63, 87, 115, 159, 217, 279, 380, 505, 657, 868, 1139, 1458, 1913, 2482, 3162, 4069, 5232, 6628, 8469, 10755, 13544, 17127, 21634, 27061, 33988, 42557, 52985, 66069, 82289, 101862, 126281, 156275, 192655, 237530, 292502

Offset: 0

Vaclav Kotesovec, Aug 19 2019

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A028377, A192065, A211856, A294842, A280541, A327064, A327065, A327066.

nmax = 50; CoefficientList[Series[Product[Product[(1+x^(k*j))^j, {j, 1, Min[k, nmax/k]}], {k, 1, nmax}], {x, 0, nmax}], x]

A327065 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(kj))^(kj)).

Original entry on oeis.org

1, 1, 2, 5, 12, 20, 42, 75, 141, 259, 466, 799, 1427, 2443, 4169, 7049, 11863, 19605, 32518, 53184, 86579, 140018, 225380, 359739, 572864, 905903, 1426270, 2234952, 3488313, 5416403, 8383226, 12917257, 19831763, 30334937, 46245977, 70242043, 106371686

Offset: 0

Vaclav Kotesovec, Aug 19 2019

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A028377, A192065, A211856, A294842, A280541, A327063, A327064, A327068.

nmax = 40; CoefficientList[Series[Product[Product[(1+x^(k*j))^(k*j), {j, 1, Min[k, nmax/k]}], {k, 1, nmax}], {x, 0, nmax}], x]

A327067 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(k*j))^k).

Original entry on oeis.org

1, 1, 3, 6, 15, 26, 57, 101, 202, 358, 670, 1165, 2113, 3614, 6326, 10691, 18275, 30408, 50969, 83716, 137943, 223883, 363547, 583369, 935524, 1485673, 2355496, 3705275, 5815497, 9066696, 14100325, 21802824, 33622951, 51592978, 78949673, 120278899, 182742752

Offset: 0

Vaclav Kotesovec, Aug 19 2019

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A000294, A061256, A182269, A279216, A280540, A327064, A327066, A327068.

nmax = 40; CoefficientList[Series[Product[Product[1/(1-x^(k*j))^k, {j, 1, Min[k, nmax/k]}], {k, 1, nmax}], {x, 0, nmax}], x]

cp's OEIS Frontend

A327063 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^j).

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A327065 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(kj))^(kj)).

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Mathematica

A327067 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(k*j))^k).

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Author

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cp's OEIS Frontend

A327063 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^j).

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Mathematica

A327065 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^(k*j)).

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Author

Keywords

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Programs

Mathematica

A327067 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(k*j))^k).

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

A327065 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(kj))^(kj)).