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

1,2

Links

Table of n, a(n) for n=1..40.

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

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

Example

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.

Prog

(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

Crossrefs

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

Cf. A305101 (number of overlined parts).

Sequence in context: A117495 A007687 A330273 * A192033 A295063 A298856

Adjacent sequences: A335663 A335664 A335665 * A335667 A335668 A335669

Keyword

nonn

Author

Jeremy Lovejoy, Jun 17 2020

Status

approved