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A335754 a(n) is the number of overpartitions of n where overlined parts are not divisible by 3 and non-overlined parts are congruent to 1 modulo 3.

%I A335754 #15 Jan 14 2021 11:46:51
%S A335754 1,2,3,4,6,9,12,17,23,30,39,51,66,84,107,135,168,209,259,319,391,478,
%T A335754 581,703,849,1022,1226,1466,1748,2078,2465,2917,3443,4055,4765,5588,
%U A335754 6540,7640,8908,10368,12047,13973,16182,18712,21604,24906,28673,32964,37846,43397
%N A335754 a(n) is the number of overpartitions of n where overlined parts are not divisible by 3 and non-overlined parts are congruent to 1 modulo 3.
%H A335754 J. Lovejoy, <a href="https://doi.org/10.1007/978-3-319-68376-8_26">Asymmetric generalizations of Schur's theorem</a>, 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.
%F A335754 G.f.: Product_{n>=1} (1+q^(3*n-1))*(1+q^(3*n-2))/(1-q^(3*n-2)).
%F A335754 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
%e A335754 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].
%t A335754 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 *)
%Y A335754 Cf. A003105, A015128, A098151, A335755.
%K A335754 nonn
%O A335754 0,2
%A A335754 _Jeremy Lovejoy_, Jun 20 2020