A335728 - OEIS

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A335728

a(n) is the number of smallest parts in the overpartitions of n having even smallest part.

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

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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