A301876 Expansion of Product_{k>=1} (1 + x^k)^A007434(k).
1, 1, 3, 11, 23, 63, 137, 329, 738, 1618, 3562, 7578, 16116, 33540, 69384, 141608, 286493, 574173, 1140355, 2247835, 4394415, 8532983, 16450061, 31513869, 59991541, 113536117, 213659967, 399910311, 744672519, 1379758479, 2544367633
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * 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(2^(5/4) * Pi / 3^(5/4) * (7/(5*Zeta(3)))^(1/4) * n^(3/4)) *(7/(15*Zeta(3)))^(1/8) / (2^(15/8) * n^(5/8)).