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Expansion of Product_{k>=1} (1 + x^k)^A000593(k).
6

%I #7 Mar 31 2018 07:01:36

%S 1,1,1,5,5,11,21,29,53,86,139,211,346,524,806,1264,1866,2838,4253,

%T 6306,9304,13751,20018,29142,42365,60900,87569,125326,178535,253371,

%U 358974,505673,710871,996658,1391551,1938801,2693543,3730901,5154610,7106235,9767649

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

%H Vaclav Kotesovec, <a href="/A301800/b301800.txt">Table of n, a(n) for n = 0..1000</a>

%F 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)).

%t 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 *)

%Y Cf. A000593, A002131, A301798, A301799.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Mar 26 2018