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A335724 a(n) is the number of smallest parts in the overpartitions of n.

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%I A335724 #13 Jun 20 2020 09:18:49
%S A335724 2,6,12,26,44,84,136,230,366,580,884,1356,2012,2968,4320,6226,8856,
%T A335724 12522,17508,24324,33528,45892,62392,84372,113374,151548,201552,
%U A335724 266752,351380,460920,601992,783158,1014984,1310600,1686408,2162814,2764748,3523324,4476720,5671748
%N A335724 a(n) is the number of smallest parts in the overpartitions of n.
%H A335724 K. Bringmann, J. Lovejoy, and R. Osburn, <a href="https://doi.org/10.1016/j.jnt.2008.10.017">Rank and crank moments for overpartitions</a>, Journal of Number Theory, 129 (2009), 1758-1772.
%H A335724 K. Bringmann, J. Lovejoy, and R. Osburn, <a href="https://doi.org/10.1093/imrn/rnp131">Automorphic properties of generating functions for generalized rank moments and Durfee symbols</a>, International Mathematics Research Notices, (2010), 238-260.
%F A335724 G.f.: 2*(Product_{k>=1} (1+q^k)/(1-q^k))*Sum_{n>=1} (q^n*Product_{j=1..n}(1-q^j))/((1-q^n)^2*Product_{j=1..n}(1+q^j)).
%F A335724 a(n) = A335728(n) + A335730(n).
%e A335724 There are 14 overpartitions of 4: [4], [4'], [3,1], [3,1'], [3',1], [3',1'], [2,2], [2',2], [2,1,1], [2,1',1], [2',1,1], [2',1',1], [1,1,1,1], [1',1,1,1], and so a(4) = 26.
%Y A335724 Cf. A015128, A092269, A235792, A335728, A335730.
%K A335724 nonn
%O A335724 1,1
%A A335724 _Jeremy Lovejoy_, Jun 19 2020