A327065 -id:A327065 - 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]

A327064 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^k).

Original entry on oeis.org

1, 1, 2, 5, 10, 18, 35, 62, 110, 197, 339, 573, 975, 1621, 2674, 4385, 7108, 11422, 18277, 28976, 45648, 71531, 111372, 172416, 265695, 407210, 621143, 943392, 1426414, 2147672, 3221271, 4812534, 7163440, 10625651, 15706871, 23141148, 33987287, 49762235

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, A327065, A327067.

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

A327068 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(kj))^(kj)).

Original entry on oeis.org

1, 1, 3, 6, 17, 28, 66, 116, 248, 441, 867, 1516, 2894, 5015, 9138, 15724, 27954, 47428, 82421, 138380, 235910, 392040, 657590, 1081225, 1789550, 2914500, 4763562, 7689071, 12433581, 19897139, 31862226, 50583981, 80285138, 126509709, 199167763, 311620226

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, A327065, A327066, A327067.

nmax = 40; CoefficientList[Series[Product[Product[1/(1-x^(k*j))^(k*j), {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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A327064 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^k).

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Author

Keywords

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Programs

Mathematica

A327068 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(kj))^(kj)).

Views

Author

Keywords

Links

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Programs

Mathematica

cp's OEIS Frontend

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

Views

Author

Keywords

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Mathematica

A327064 Expansion of Product_{k>=1} (Product_{j=1..k} (1 + x^(k*j))^k).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A327068 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(k*j))^(k*j)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A327068 Expansion of Product_{k>=1} (Product_{j=1..k} 1/(1 - x^(kj))^(kj)).