A303392 Expansion of Product_{k>=1} ((1 + 4*x^k) / (1 - 4*x^k))^(1/2).

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

Links

Table of n, a(n) for n=0..25.

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

Cf. A261568, A246936, A067855, A303350, A303391, A303360.

Sequence in context: A149402 A045906 A025282 * A149403 A127866 A149404

Adjacent sequences: A303389 A303390 A303391 * A303393 A303394 A303395

Keyword

nonn

Author

Vaclav Kotesovec, Apr 23 2018

Status

approved