A301875 Expansion of Product_{k>=1} 1/(1 - x^k)^A007434(k).

1, 1, 4, 12, 30, 78, 184, 448, 1033, 2361, 5292, 11676, 25382, 54470, 115508, 242132, 502520, 1032632, 2103172, 4246948, 8507968, 16915536, 33391788, 65470332, 127539321, 246928233, 475274592, 909658536, 1731703788, 3279644604, 6180528236

Offset: 0

Author

Vaclav Kotesovec, Mar 28 2018

Keywords

• nonn

Comments

Euler transform of A007434.

Links

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

Crossrefs

Cf. A007434, A061255, A301876.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[Sum[Sum[d^2 MoebiusMu[k/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(4*Pi*n^(3/4) / (3^(5/4) * (5*Zeta(3))^(1/4)) + Zeta(3) / (2*Pi^2)) / (2^(3/2) * (15*Zeta(3))^(1/8) * n^(5/8)).