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A303346 Expansion of Product_{n>=1} ((1 + 2*x^n)/(1 - 2*x^n))^(1/2). 5
1, 2, 4, 10, 18, 38, 72, 142, 260, 510, 940, 1814, 3362, 6490, 12112, 23466, 44114, 85766, 162516, 317190, 604806, 1184682, 2271248, 4461514, 8591784, 16916490, 32696708, 64496130, 125037142, 247007142, 480077432, 949510526, 1849375796, 3661330398, 7144215452 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

FORMULA

a(n) ~ 2^n / sqrt(c*Pi*n), where c = A048651 * A083864 = 1/2 * Product_{j>=1} (2^j-1)/(2^j+1) = 0.06056210400129025123042464659093375290492912341... - Vaclav Kotesovec, Apr 22 2018

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[((1 + 2*x^k)/(1 - 2*x^k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)

nmax = 30; CoefficientList[Series[Sqrt[-QPochhammer[-2, x] / (3*QPochhammer[2, x])], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)

PROG

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

CROSSREFS

Cf. A032302, A070933, A261584, A303307, A303345.

Sequence in context: A189892 A240877 A218008 * A197049 A303438 A104723

Adjacent sequences:  A303343 A303344 A303345 * A303347 A303348 A303349

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 22 2018

STATUS

approved

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)