login
A318764
Expansion of Product_{i>=1, j>=1, k>=1} ((1 + x^(i*j*k))/(1 - x^(i*j*k)))^(i*j*k).
1
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
0,2
COMMENTS
Convolution of A318413 and A318414.
LINKS
FORMULA
Conjecture: log(a(n)) ~ (21*Zeta(3))^(1/3) * log(n)^(2/3) * n^(2/3) / 2^(5/3).
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 03 2018
STATUS
approved