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A335724 a(n) is the number of smallest parts in the overpartitions of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)