A333653 Expansion of Product_{i>=1, j>=1} (1 + i*x^(i*j)).

1, 1, 3, 7, 13, 27, 54, 98, 174, 335, 572, 1004, 1733, 2933, 4916, 8307, 13470, 22042, 35851, 57256, 91462, 145231, 227667, 355522, 554058, 853986, 1313121, 2010318, 3057827, 4627213, 6989808, 10481205, 15679549, 23365207, 34658909, 51241077, 75541695, 110852295, 162238415

Offset: 0

Author

Seiichi Manyama, Aug 23 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A022629, A107742, A285244, A318416, A332199.

Programs

Mathematica

m = 38; CoefficientList[Series[Product[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(prod(i=1, N, prod(j=1, N\i, 1+i*x^(i*j))))

PARI

N=40; x='x+O('x^N); Vec(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 + i*q^i).

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