A335666 a(n) is the sum, over all overpartitions of n, of the overlined parts.

1, 3, 10, 21, 46, 90, 168, 295, 511, 850, 1382, 2198, 3430, 5260, 7960, 11861, 17468, 25445, 36670, 52346, 74092, 103986, 144840, 200322, 275191, 375662, 509816, 687960, 923442, 1233340, 1639312, 2168999, 2857460, 3748772, 4898652, 6377023, 8271294, 10690830, 13771912, 17683642

Offset: 1

Author

Jeremy Lovejoy, Jun 17 2020

Keywords

• nonn

Examples

			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.
		

Links

• K. Bringmann, J. Lovejoy, and R. Osburn, Rank and crank moments for overpartitions, Journal of Number Theory, 129 (2009), 1758-1772.

Crossrefs

Cf. A015128, A230441, A235790, A235792, A235793, A235798, A236000, A236001, A237047, A335651.

Cf. A305101 (number of overlined parts).

Programs

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

Formula

G.f.: (Product_{k>=1} (1+q^k)/(1-q^k)) * Sum_{n>=1} n*q^n/(1+q^n).

a(n) = A235793(n) - A335651(n). - Omar E. Pol, Jun 17 2020