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%I #12 Aug 24 2021 06:59:56
%S 1,0,2,2,4,4,8,10,16,20,30,38,54,68,94,120,160,202,266,334,432,540,
%T 688,856,1080,1334,1668,2052,2542,3110,3828,4660,5698,6906,8394,10130,
%U 12250,14720,17716,21210,25412,30310,36172,42994,51114,60558,71740,84732,100052
%N The number of overpartitions of n whose Frobenius symbols have only odd parts in the top row.
%C a(n) is also the excess of the number of overpartitions of n with an even number of non-overlined parts larger than the number of overlined parts over the number of overpartitions of n with an odd number of non-overlined parts larger than the number of overlined parts.
%H B. Kim, E. Kim, and J. Lovejoy, <a href="https://doi.org/10.1142/S1793042120400345">On weighted overpartitions related to some q-series in Ramanujan's lost notebook</a>, Int. J. Number Theory 17 (2021), 603-619.
%F G.f.: (Product_{k>=1} 1/(1-q^k))*Sum_{n>=0} q^(n*(3*n+1)/2)*(1-q^(2*n+1)).
%Y Cf. A015128, A143184, A347207.
%K nonn
%O 0,3
%A _Jeremy Lovejoy_, Aug 23 2021