A303438 - OEIS

%I #19 Apr 25 2018 07:51:12

%S 1,2,4,10,18,38,80,158,292,630,1260,2470,4922,9706,19392,41010,78466,

%T 155494,318764,625670,1238854,2567666,5106208,10122522,20022960,

%U 40082154,80027140,163330106,324201942,643489014,1306843568,2592220110,5081546084

%N Expansion of Product_{k>=1} ((1 + 2^k*x^k)/(1 - 2^k*x^k))^(1/2^k).

%C a(n) / 2^n tends to 1.2036... - _Vaclav Kotesovec_, Apr 25 2018

%H Seiichi Manyama, <a href="/A303438/b303438.txt">Table of n, a(n) for n = 0..3000</a>

%H Vaclav Kotesovec, <a href="/A303438/a303438.jpg">Graph - The asymptotic ratio</a>

%F G.f.: exp(Sum_{j>=1} ((-1)^j - 1) / (j*(1 - 1/(2^(j-1)*x^j))) )). - _Vaclav Kotesovec_, Apr 25 2018

%t nmax = 30; CoefficientList[Series[Product[((1 + 2^k*x^k)/(1 - 2^k*x^k))^(1/2^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 24 2018 *)

%t nmax = 30; CoefficientList[Series[Exp[Sum[((-1)^j - 1) / (j*(1 - 1/(2^(j - 1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 25 2018 *)

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+2^k*x^k)/(1-2^k*x^k))^(1/2^k)))

%Y Cf. A015128, A303346, A303360, A303382, A303439.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 24 2018