A303360 Expansion of Product_{n>=1} ((1 + 4*x^n)/(1 - 4*x^n))^(1/4).
1, 2, 4, 18, 34, 166, 384, 1902, 4756, 24022, 64284, 321542, 899658, 4455690, 12888944, 63185250, 187513426, 910880550, 2759413788, 13295839638, 40967821494, 195979968882, 612569599440, 2911592648458, 9213101043936, 43538337410474, 139246245625364
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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Maple
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
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Mathematica
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 *) nmax = 30; CoefficientList[Series[(-3*QPochhammer[-4, x] / (5*QPochhammer[4, x]))^(1/4), {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 23 2018 *) -
PARI
N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+4*x^k)/(1-4*x^k))^(1/4)))
Formula
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