A321240 Expansion of Product_{i>=1, j>=1, k>=1, l>=1} (1 + x^(i*j*k*l))/(1 - x^(i*j*k*l)).

1, 2, 10, 26, 86, 210, 594, 1394, 3530, 8006, 18842, 41258, 92190, 195714, 419538, 867050, 1797568, 3625758, 7311382, 14431294, 28416514, 55010142, 106101558, 201814518, 382213566, 715473554, 1333083950, 2459265058, 4515151234, 8218572030, 14888270366, 26766878302

Offset: 0

Author

Seiichi Manyama, Nov 01 2018

Keywords

• nonn

Comments

Convolution of the sequences A280486 and A280487.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007426, A015128, A280486, A280487, A301554, A305050.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(   (&*[(&*[(&*[(&*[(1+x^(i*j*k*l))/(1-x^(i*j*k*l)): i in [1..m]]): j in [1..m]]): k in [1..m]]): l in [1..m]]))); // G. C. Greubel, Nov 01 2018

Mathematica

With[{nmax=50}, CoefficientList[Series[Product[(1 + x^(i*j*k*l))/(1 - x^(i*j*k*l)), {i,1,nmax}, {j,1,nmax/i}, {k,1,nmax/i/j}, {l,1,nmax/i/j/k}], {x,0,nmax}], x]] (* G. C. Greubel, Nov 01 2018 *)

PARI

m=50; x='x+O('x^m); Vec(prod(k=1,m, ((1+x^k)/(1-x^k))^ sumdiv(k, d, numdiv(k/d)*numdiv(d)))) \\ G. C. Greubel, Nov 01 2018

Formula

G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A007426(k).