A309240 Expansion of 1/((1 - x)*(1 - x^2)*(1 + x^3)*(1 + x^4)*(1 - x^5)*(1 - x^6)*(1 + x^7)*(1 + x^8)*...).

1, 1, 2, 1, 1, 1, 3, 3, 4, 2, 4, 4, 7, 5, 7, 6, 11, 9, 13, 10, 17, 14, 20, 15, 25, 22, 32, 24, 36, 31, 48, 38, 55, 45, 68, 55, 79, 65, 97, 79, 112, 91, 136, 113, 159, 128, 186, 156, 221, 179, 256, 213, 301, 245, 347, 290, 409, 334, 466, 388, 547, 451, 624, 517, 724, 600, 828, 687, 955, 793, 1088

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>=1} 1/(1 + (-1)^(k*(k+1)/2) * x^k).

G.f.: Product_{k>=1} (1 + x^(4*k-2)) / ((1 + x^(4*k-1)) * (1 - x^(4*k-3))).

a(n) ~ Gamma(1/4) * exp(Pi*sqrt(n/6)) / (4 * 6^(1/8) * Pi^(3/4) * n^(5/8)). - Vaclav Kotesovec, Jul 17 2019

Mathematica

nmax = 70; CoefficientList[Series[Product[1/(1 + (-1)^(k (k + 1)/2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k - 2))/((1 + x^(4 k - 1)) (1 - x^(4 k - 3))), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[2/(QPochhammer[-1, -x^2] QPochhammer[x, -x^2]), {x, 0, nmax}], x]

Crossrefs

Cf. A000700, A035451, A147599, A300574.

Sequence in context: A344678 A079415 A126347 * A057001 A307689 A299037

Adjacent sequences: A309237 A309238 A309239 * A309241 A309242 A309243

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 17 2019

Status

approved