A301978 - OEIS

%I #10 Mar 31 2018 07:23:11

%S 1,1,6,16,51,127,367,897,2342,5662,13894,32656,77076,176586,403526,

%T 904140,2013267,4418167,9628682,20741434,44362988,93984842,197731390,

%U 412619250,855408327,1760687593,3601827236,7321181534,14796204874,29730215150,59419375058

%N Euler transform of A065958.

%H Vaclav Kotesovec, <a href="/A301978/b301978.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{k>=1} 1/(1-x^k)^A065958(k).

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

%t nmax = 40; CoefficientList[Series[Exp[Sum[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, A301980.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 30 2018