OFFSET
0,2
LINKS
J. Lovejoy, Asymmetric generalizations of Schur's theorem, in: Andrews G., Garvan F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham.
FORMULA
G.f.: Product_{n>=1} (1+q^(3*n-1))*(1+q^(3*n-2))/(1-q^(3*n-2)).
a(n) ~ Gamma(1/3) * exp(2*Pi*sqrt(n)/3) / (2^(3/2) * sqrt(3) * Pi^(2/3) * n^(2/3)). - Vaclav Kotesovec, Jan 14 2021
EXAMPLE
The 9 overpartitions counted by a(5) are: [5'], [4,1], [4,1'], [4',1], [4',1'], [2',1,1,1], [2',1',1,1], [1,1,1,1,1], [1',1,1,1,1].
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1 + x^(3*k-1)) * (1 + x^(3*k-2)) / (1 - x^(3*k-2)), {k, 1, nmax/3}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 14 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeremy Lovejoy, Jun 20 2020
STATUS
approved