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A303360 Expansion of Product_{n>=1} ((1 + 4*x^n)/(1 - 4*x^n))^(1/4). 6

%I

%S 1,2,4,18,34,166,384,1902,4756,24022,64284,321542,899658,4455690,

%T 12888944,63185250,187513426,910880550,2759413788,13295839638,

%U 40967821494,195979968882,612569599440,2911592648458,9213101043936,43538337410474,139246245625364

%N Expansion of Product_{n>=1} ((1 + 4*x^n)/(1 - 4*x^n))^(1/4).

%H Seiichi Manyama, <a href="/A303360/b303360.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ c * 4^n / n^(3/4), where c = (QPochhammer[-1, 1/4] / QPochhammer[1/4])^(1/4) / Gamma(1/4) = 0.3885547372628... - _Vaclav Kotesovec_, Apr 23 2018

%p seq(coeff(series(mul(((1+4*x^k)/(1-4*x^k))^(1/4), k = 1..n), x, n+1), x, n), n = 0..35); # _Muniru A Asiru_, Apr 22 2018

%t nmax = 30; CoefficientList[Series[Product[((1 + 4*x^k)/(1 - 4*x^k))^(1/4), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 22 2018 *)

%t nmax = 30; CoefficientList[Series[(-3*QPochhammer[-4, x] / (5*QPochhammer[4, x]))^(1/4), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 23 2018 *)

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+4*x^k)/(1-4*x^k))^(1/4)))

%Y Expansion of Product_{n>=1} ((1 + 2^b*x^n)/(1 - 2^b*x^n))^(1/(2^b)): A015128 (b=0), A303346 (b=1), this sequence (b=2).

%Y Cf. A303361, A303391, A067855, A303350, A303392.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 22 2018

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)