A332199 Expansion of Product_{i>=1, j>=1} 1/(1 - i*x^(i*j)).

1, 1, 4, 8, 22, 40, 101, 183, 412, 765, 1586, 2899, 5834, 10484, 20199, 36246, 67758, 119837, 219661, 384200, 690164, 1197423, 2114105, 3632088, 6332797, 10779478, 18555115, 31354932, 53385037, 89494901, 150983344, 251284829, 420218575, 694947117, 1152915743, 1894656801

Offset: 0

Author

Seiichi Manyama, Aug 23 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006171, A006906, A285245, A318415, A333653.

Programs

Mathematica

m = 35; CoefficientList[Series[Product[1/(1 - i*x^(i*j)), {i, 1, m}, {j, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Aug 23 2020 *)

PARI

N=40; x='x+O('x^N); Vec(1/prod(i=1, N, prod(j=1, N\i, 1-i*x^(i*j))))

PARI

N=40; x='x+O('x^N); Vec(1/prod(k=1, N, prod(d=1, k, 1-(k%d==0)*d*x^k)))

Formula

G.f.: Product_{k>0} f(q^k) where f(q) = Product_{i>=1} 1/(1 - i*q^i).

G.f.: Product_{k>0} Product_{d|k} 1/(1 - d*x^k).