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A335666 a(n) is the sum, over all overpartitions of n, of the overlined parts. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)