A305050 Expansion of Product_{i>=1, j>=1, k>=1} (1 + x^(i*j*k))/(1 - x^(i*j*k)).

1, 2, 8, 20, 56, 128, 316, 684, 1532, 3192, 6704, 13436, 26984, 52352, 101316, 191320, 359334, 662292, 1213360, 2189380, 3925432, 6951592, 12231332, 21298452, 36856840, 63211164, 107765896, 182295468, 306625208, 512190992, 851011960, 1405199028, 2308629300, 3771593392

Offset: 0

Author

Ilya Gutkovskiy, May 24 2018

Keywords

• nonn

Comments

Convolution of the sequences A174465 and A280473.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Transforms
• Index entries for sequences related to partitions

Crossrefs

Cf. A007425, A174465, A280473, A301554.

Programs

Mathematica

nmax = 33; CoefficientList[Series[Product[(1 + x^(i j k))/(1 - x^(i j k)), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}], {x, 0, nmax}], x]
nmax = 33; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A007425(k).