|
%I #17 Jun 18 2020 03:24:46
%S 1,3,10,21,46,90,168,295,511,850,1382,2198,3430,5260,7960,11861,17468,
%T 25445,36670,52346,74092,103986,144840,200322,275191,375662,509816,
%U 687960,923442,1233340,1639312,2168999,2857460,3748772,4898652,6377023,8271294,10690830,13771912,17683642
%N a(n) is the sum, over all overpartitions of n, of the overlined parts.
%H 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.
%F G.f.: (Product_{k>=1} (1+q^k)/(1-q^k)) * Sum_{n>=1} n*q^n/(1+q^n).
%F a(n) = A235793(n) - A335651(n). - _Omar E. Pol_, Jun 17 2020
%e The 8 overpartitions of 8 are [3], [3'], [2,1], [2,1'], [2',1], [2',1'], [1,1,1], [1',1,1], and so a(3) = 10.
%o (PARI) my(N=44, q='q+O('q^N)); Vec( prod(k=1,N, (1+q^k)/(1-q^k)) * sum(k=1,N, k*q^k/(1+q^k)) ) \\ _Joerg Arndt_, Jun 18 2020
%Y Cf. A015128, A230441, A235790, A235792, A235793, A235798, A236000, A236001, A237047, A335651.
%Y Cf. A305101 (number of overlined parts).
%K nonn
%O 1,2
%A _Jeremy Lovejoy_, Jun 17 2020
|
