A301594 Expansion of Product_{k>=1} (1 + x^k)^A001615(k), where A001615 is the Dedekind psi function.

1, 1, 3, 7, 13, 27, 55, 99, 185, 341, 604, 1064, 1863, 3181, 5411, 9123, 15167, 25051, 41083, 66715, 107703, 172735, 275034, 435484, 685753, 1073481, 1672160, 2592070, 3998278, 6140196, 9389302, 14296376, 21682534, 32759202, 49308812, 73956692, 110545113

Offset: 0

Author

Vaclav Kotesovec, Mar 24 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A001615, A156303.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[k*Sum[MoebiusMu[d]^2 / d, {d, Divisors @ 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^(5/3) * (5*Zeta(3))^(1/3) * n^(2/3) / (2^(4/3) * Pi^(2/3)) - Pi^(2/3) * n^(1/3) / (2^(5/3) * 3^(2/3) * (5*Zeta(3))^(1/3)) - Pi^2 / (2160 * Zeta(3))) * (5*Zeta(3))^(1/6) / (2^(3/4) * 3^(1/6) * Pi^(5/6) * n^(2/3)).