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A303392
Expansion of Product_{k>=1} ((1 + 4*x^k) / (1 - 4*x^k))^(1/2).
1
1, 4, 12, 52, 156, 612, 2028, 7892, 27324, 107396, 384844, 1520436, 5566876, 22069796, 81990252, 325707348, 1222582268, 4862950020, 18395472460, 73233825524, 278700724764, 1110232691108, 4245596648876, 16920914168148, 64963831455996, 259012955299396
OFFSET
0,2
FORMULA
a(n) ~ sqrt(c) * 4^n / sqrt(Pi*n), where c = QPochhammer[-1, 1/4]/QPochhammer[1/4] = 3.9385207073365388638943873939345313401323799...
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[((1+4*x^k)/(1-4*x^k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 30; CoefficientList[Series[(-3*QPochhammer[-4, x] / (5*QPochhammer[4, x]))^(1/2), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 23 2018
STATUS
approved