A320236 -id:A320236 - cp's OEIS frontend

A320235 G.f.: Product_{k>=1, j>=1} (1 + x^(k*j))^2.

1, 2, 5, 12, 24, 48, 94, 172, 310, 550, 946, 1602, 2679, 4394, 7123, 11424, 18082, 28344, 44039, 67754, 103412, 156660, 235489, 351602, 521650, 768998, 1127100, 1642946, 2381929, 3436028, 4932998, 7049004, 10028422, 14207122, 20044327, 28169528, 39439899

Offset: 0

Vaclav Kotesovec, Oct 08 2018

nonn

Self-convolution of A107742.

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

Cf. A107742, A280451, A320236.

nmax = 50; CoefficientList[Series[Product[(1+x^(k*j))^2, {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x]

Conjecture: log(a(n)) ~ Pi*sqrt(n*log(n)/3).

A320238 G.f.: Product_{k>=1, j>=1} (1 + x^(kj)) / (1 - x^(kj))^2.

Original entry on oeis.org

1, 3, 11, 31, 85, 209, 504, 1138, 2514, 5339, 11098, 22432, 44535, 86523, 165496, 311187, 577190, 1055524, 1907423, 3405574, 6016826, 10520065, 18222215, 31275320, 53230224, 89860112, 150551503, 250388180, 413572707, 678574627, 1106396434, 1793009335

Offset: 0

Vaclav Kotesovec, Oct 08 2018

nonn

Convolution of A107742 and A320236.

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

Cf. A158441, A107742, A320236.

nmax = 50; CoefficientList[Series[Product[(1+x^(k*j))/(1-x^(k*j))^2, {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x]

Conjecture: log(a(n)) ~ Pi * sqrt(5*n*log(n)/6).

A320237 G.f.: Product_{k>=1, j>=1} ((1 + x^(kj)) / (1 - x^(kj)))^2.

Original entry on oeis.org

1, 4, 16, 52, 156, 428, 1120, 2772, 6616, 15224, 34032, 74020, 157340, 327244, 667824, 1338828, 2641332, 5133372, 9840432, 18621476, 34818852, 64374564, 117768176, 213306948, 382733816, 680630120, 1200198784, 2099417544, 3644332860, 6280017740, 10746594208

Offset: 0

Vaclav Kotesovec, Oct 08 2018

nonn

Self-convolution of A301554.

Convolution of A320235 and A320236.

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

Cf. A301554, A320235, A320236.

nmax = 40; CoefficientList[Series[Product[((1+x^(k*j))/(1-x^(k*j)))^2, {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x]

Conjecture: log(a(n)) ~ Pi * sqrt(n*log(n)).

A320245 G.f.: Product_{k>=1, j>=1} 1/((1 + x^(kj)) (1 - x^(k*j))^2).

Original entry on oeis.org

1, 1, 4, 6, 17, 25, 59, 89, 187, 284, 545, 828, 1505, 2270, 3930, 5904, 9861, 14695, 23827, 35248, 55775, 81882, 126874, 184870, 281467, 407065, 610193, 876282, 1295892, 1848144, 2700398, 3825912, 5530337, 7786022, 11145541, 15597196, 22131170, 30792303

Offset: 0

Vaclav Kotesovec, Oct 08 2018

nonn

Convolution of A288007 and A320236.

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

Cf. A158441, A320236, A320238.

nmax = 50; CoefficientList[Series[Product[1/((1+x^(k*j))*(1-x^(k*j))^2), {k, 1, nmax}, {j, 1, Floor[nmax/k]+1}], {x, 0, nmax}], x]

cp's OEIS Frontend

A320235 G.f.: Product_{k>=1, j>=1} (1 + x^(k*j))^2.

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A320238 G.f.: Product_{k>=1, j>=1} (1 + x^(kj)) / (1 - x^(kj))^2.

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A320237 G.f.: Product_{k>=1, j>=1} ((1 + x^(kj)) / (1 - x^(kj)))^2.

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A320245 G.f.: Product_{k>=1, j>=1} 1/((1 + x^(kj)) (1 - x^(k*j))^2).

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cp's OEIS Frontend

A320235 G.f.: Product_{k>=1, j>=1} (1 + x^(k*j))^2.

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A320238 G.f.: Product_{k>=1, j>=1} (1 + x^(k*j)) / (1 - x^(k*j))^2.

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A320237 G.f.: Product_{k>=1, j>=1} ((1 + x^(k*j)) / (1 - x^(k*j)))^2.

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A320245 G.f.: Product_{k>=1, j>=1} 1/((1 + x^(k*j)) * (1 - x^(k*j))^2).

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A320238 G.f.: Product_{k>=1, j>=1} (1 + x^(kj)) / (1 - x^(kj))^2.

A320237 G.f.: Product_{k>=1, j>=1} ((1 + x^(kj)) / (1 - x^(kj)))^2.

A320245 G.f.: Product_{k>=1, j>=1} 1/((1 + x^(kj)) (1 - x^(k*j))^2).