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A335728 a(n) is the number of smallest parts in the overpartitions of n having even smallest part. 2
0, 2, 0, 6, 4, 12, 12, 30, 36, 60, 80, 132, 180, 264, 360, 522, 712, 990, 1344, 1844, 2472, 3324, 4420, 5892, 7764, 10212, 13344, 17400, 22556, 29160, 37524, 48166, 61560, 78456, 99648, 126234, 159396, 200740, 252096, 315828 (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.

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^(2*n)*Product_{j=1..2*n}(1-q^j))/((1-q^(2*n))^2*Product_{j=1..2*n}(1+q^j)).

a(n) = A335724(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) = 6.

CROSSREFS

Cf. A015128, A092269, A235792, A335724, A335730.

Sequence in context: A124228 A115879 A115880 * A078037 A088508 A142457

Adjacent sequences:  A335725 A335726 A335727 * A335729 A335730 A335731

KEYWORD

nonn

AUTHOR

Jeremy Lovejoy, Jun 19 2020

STATUS

approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)