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

0,3

Links

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

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)).

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 *)

Crossrefs

Cf. A007434, A299069, A301875.

Sequence in context: A165635 A376753 A337476 * A032026 A282198 A158034

Adjacent sequences: A301873 A301874 A301875 * A301877 A301878 A301879

Keyword

nonn

Author

Vaclav Kotesovec, Mar 28 2018

Status

approved