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

2, 6, 12, 26, 44, 84, 136, 230, 366, 580, 884, 1356, 2012, 2968, 4320, 6226, 8856, 12522, 17508, 24324, 33528, 45892, 62392, 84372, 113374, 151548, 201552, 266752, 351380, 460920, 601992, 783158, 1014984, 1310600, 1686408, 2162814, 2764748, 3523324, 4476720, 5671748

Offset

1,1

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.

K. Bringmann, J. Lovejoy, and R. Osburn, Automorphic properties of generating functions for generalized rank moments and Durfee symbols, International Mathematics Research Notices, (2010), 238-260.

Formula

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)).

a(n) = A335728(n) + A335730(n).

Example

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.

Crossrefs

Cf. A015128, A092269, A235792, A335728, A335730.

Sequence in context: A034875 A136515 A141347 * A300120 A246584 A054454

Adjacent sequences: A335721 A335722 A335723 * A335725 A335726 A335727

Keyword

nonn

Author

Jeremy Lovejoy, Jun 19 2020

Status

approved