A318764 Expansion of Product_{i>=1, j>=1, k>=1} ((1 + x^(i*j*k))/(1 - x^(i*j*k)))^(i*j*k).

1, 2, 14, 44, 182, 548, 1932, 5632, 17654, 49872, 145020, 395256, 1090044, 2876424, 7606024, 19503312, 49850790, 124543772, 309436980, 755268832, 1831194724, 4376807896, 10387118328, 24359228520, 56720659372, 130737105940, 299256890672, 678941040784

Offset: 0

Author

Vaclav Kotesovec, Sep 03 2018

Keywords

• nonn

Comments

Convolution of A318413 and A318414.

Links

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

Crossrefs

Cf. A318413, A318414.

Cf. A156616, A318579.

Cf. A015128, A305050.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[Product[Product[((1 + x^(i*j*k))/(1 - x^(i*j*k)))^(i*j*k), {i, 1, nmax/j/k}], {j, 1, nmax/k}], {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(k*Sum[DivisorSigma[0, d], {d, Divisors[k]}]), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

Conjecture: log(a(n)) ~ (21*Zeta(3))^(1/3) * log(n)^(2/3) * n^(2/3) / 2^(5/3).