A303438 Expansion of Product_{k>=1} ((1 + 2^k*x^k)/(1 - 2^k*x^k))^(1/2^k).

1, 2, 4, 10, 18, 38, 80, 158, 292, 630, 1260, 2470, 4922, 9706, 19392, 41010, 78466, 155494, 318764, 625670, 1238854, 2567666, 5106208, 10122522, 20022960, 40082154, 80027140, 163330106, 324201942, 643489014, 1306843568, 2592220110, 5081546084

Offset: 0

Author

Seiichi Manyama, Apr 24 2018

Keywords

• nonn

Comments

a(n) / 2^n tends to 1.2036... - Vaclav Kotesovec, Apr 25 2018

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000
• Vaclav Kotesovec, Graph - The asymptotic ratio

Crossrefs

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

Programs

Mathematica

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 *)
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 *)

PARI

my(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)))

Formula

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