A303391 Expansion of Product_{k>=1} (1 + 4*x^k)/(1 - 4*x^k).

1, 8, 40, 200, 872, 3720, 15400, 62920, 254440, 1024648, 4112680, 16483400, 66000360, 264150920, 1056903080, 4228272200, 16914393832, 67660396040, 270647139240, 1082600410440, 4330424811880, 17321748357640, 69287088965800, 277148557003720, 1108594618342760

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1600

Formula

a(n) ~ c * 4^n, where c = QPochhammer[-1, 1/4] / QPochhammer[1/4] = 3.9385207073365388638943873939345313401323799...

Maple

N:= 50: # for a(0)..a(N)
G:= mul((1+4*x^k)/(1-4*x^k), k=1..N):
S:= series(G, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Feb 13 2019

Mathematica

nmax = 25; CoefficientList[Series[Product[(1+4*x^k)/(1-4*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A261568, A246936, A067855, A303350.

Cf. A015128, A261584, A303390.

Sequence in context: A270947 A271595 A270283 * A270730 A128625 A037598

Adjacent sequences: A303388 A303389 A303390 * A303392 A303393 A303394

Keyword

nonn

Author

Vaclav Kotesovec, Apr 23 2018

Status

approved