A320244 G.f.: Product_{k>=1, j>=1} (1 + x^(k*j))^2 / (1 - x^(k*j)).

1, 3, 10, 28, 72, 172, 397, 867, 1840, 3783, 7580, 14829, 28454, 53540, 99119, 180676, 324758, 576145, 1010051, 1750782, 3003386, 5101769, 8586891, 14327582, 23711567, 38937304, 63471475, 102741924, 165204561, 263956121, 419183458, 661833319, 1039140705

Offset: 0

Author

Vaclav Kotesovec, Oct 08 2018

Keywords

• nonn

Comments

Convolution of A006171 and A320235.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006171, A320235, A320238.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^(k*j))^2/(1-x^(k*j)), {k, 1, nmax}, {j, 1, Floor[nmax/k]+1}], {x, 0, nmax}], x]

Formula

Conjecture: log(a(n)) ~ Pi * sqrt(2*n*log(n)/3).