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 A303438 Expansion of Product_{k>=1} ((1 + 2^k*x^k)/(1 - 2^k*x^k))^(1/2^k). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 FORMULA G.f.: exp(Sum_{j>=1} ((-1)^j - 1) / (j*(1 - 1/(2^(j-1)*x^j))) )). - Vaclav Kotesovec, Apr 25 2018 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 *) PROG (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))) CROSSREFS Cf. A015128, A303346, A303360, A303382, A303439. Sequence in context: A218008 A303346 A197049 * A348396 A104723 A206140 Adjacent sequences: A303435 A303436 A303437 * A303439 A303440 A303441 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 24 2018 STATUS approved

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Last modified June 8 02:04 EDT 2023. Contains 363157 sequences. (Running on oeis4.)