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A293306
Expansion of (eta(q)eta(q^3))/eta(q^2)^2 in powers of q.
4
1, -1, 1, -3, 4, -5, 6, -9, 13, -16, 20, -27, 36, -44, 54, -69, 88, -107, 130, -162, 200, -240, 288, -351, 426, -507, 602, -723, 864, -1019, 1200, -1422, 1681, -1968, 2300, -2700, 3160, -3674, 4266, -4965, 5768, -6665, 7692, -8892, 10260, -11792, 13536, -15552
OFFSET
0,4
LINKS
FORMULA
G.f.: Product_{i>0} (1 + Sum_{j>0} (-1)^j*j*q^(j*i)).
a(n) ~ (-1)^n * exp(2*Pi*sqrt(n)/3) / (6*n^(3/4)). - Vaclav Kotesovec, Oct 05 2017
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 - x^k) * (1 - x^(3*k)) / (1 - x^(2*k))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 05 2017 *)
CROSSREFS
Main diagonal of A293305.
Cf. A122792.
Sequence in context: A105857 A103055 A128995 * A014101 A039035 A065798
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 05 2017
STATUS
approved