A301980 - OEIS

%I #7 Mar 31 2018 07:22:27

%S 1,1,5,15,40,106,281,685,1690,4050,9496,21908,49902,111740,247465,

%T 541353,1171070,2507602,5319085,11178947,23298878,48169708,98834943,

%U 201335651,407345067,818767703,1635528657,3247634227,6412057831,12590738729,24593652845

%N Expansion of Product_{k>=1} (1 + x^k)^A065958(k).

%H Vaclav Kotesovec, <a href="/A301980/b301980.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ exp(2^(5/4) * sqrt(7) * Zeta(3)^(1/4) * n^(3/4) / sqrt(3*Pi) - sqrt(Pi) * n^(1/4) / (2^(9/4) * 3^(3/2) * sqrt(7) * Zeta(3)^(1/4))) * 21^(1/4) * Zeta(3)^(1/8) / (2^(15/8) * Pi^(3/4) * n^(5/8)).

%t nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[Sum[MoebiusMu[k/d]^2*d^2, {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 *)

%Y Cf. A065958, A156733, A301978.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 30 2018