A320238 -id:A320238 - cp's OEIS frontend

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

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]

A320244 G.f.: Product_{k>=1, j>=1} (1 + x^(kj))^2 / (1 - x^(kj)).

Original entry on oeis.org

1, 3, 10, 28, 72, 172, 397, 867, 1840, 3783, 7580, 14829, 28454, 53540, 99119, 180676, 324758, 576145, 1010051, 1750782, 3003386, 5101769, 8586891, 14327582, 23711567, 38937304, 63471475, 102741924, 165204561, 263956121, 419183458, 661833319, 1039140705

Offset: 0

Vaclav Kotesovec, Oct 08 2018

nonn

Convolution of A006171 and A320235.

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

Cf. A006171, A320235, A320238.

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

Conjecture: log(a(n)) ~ Pi * sqrt(2*n*log(n)/3).

cp's OEIS Frontend

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

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A320244 G.f.: Product_{k>=1, j>=1} (1 + x^(kj))^2 / (1 - x^(kj)).

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cp's OEIS Frontend

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

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A320244 G.f.: Product_{k>=1, j>=1} (1 + x^(k*j))^2 / (1 - x^(k*j)).

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Mathematica

Formula

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

A320244 G.f.: Product_{k>=1, j>=1} (1 + x^(kj))^2 / (1 - x^(kj)).