A301800 Expansion of Product_{k>=1} (1 + x^k)^A000593(k).

1, 1, 1, 5, 5, 11, 21, 29, 53, 86, 139, 211, 346, 524, 806, 1264, 1866, 2838, 4253, 6306, 9304, 13751, 20018, 29142, 42365, 60900, 87569, 125326, 178535, 253371, 358974, 505673, 710871, 996658, 1391551, 1938801, 2693543, 3730901, 5154610, 7106235, 9767649

Offset: 0

Author

Vaclav Kotesovec, Mar 26 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000593, A002131, A301798, A301799.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[DivisorSum[k, -(-1)^# k / # &] * 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 * Pi^(2/3) * Zeta(3)^(1/3) * n^(2/3)/4) * Zeta(3)^(1/6) / (2^(25/24) * sqrt(3) * Pi^(1/6) * n^(2/3)).