A301798 Expansion of Product_{k>=1} (1 + x^k)^A002131(k).

1, 1, 2, 6, 9, 19, 36, 62, 110, 197, 332, 559, 947, 1548, 2538, 4133, 6610, 10536, 16710, 26191, 40879, 63465, 97732, 149852, 228658, 346788, 523694, 787503, 1178325, 1756294, 2607686, 3855676, 5680851, 8341007, 12202794, 17795283, 25869297, 37487313

Offset: 0

Author

Vaclav Kotesovec, Mar 26 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000203, A002131, A192065.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[DivisorSum[k, # / GCD[#, 2] &] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)

Formula

a(n) ~ exp(3^(4/3) * Pi^(2/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(7/3) - Pi^(4/3) * n^(1/3) / (2^(8/3) * 3^(4/3) * Zeta(3)^(1/3)) - Pi^2 / (2592 * Zeta(3))) * Zeta(3)^(1/6) / (2^(7/6) * 3^(1/3) * Pi^(1/6) * n^(2/3)).