A335730 a(n) is the number of smallest parts in the overpartitions of n having odd smallest part.

2, 4, 12, 20, 40, 72, 124, 200, 330, 520, 804, 1224, 1832, 2704, 3960, 5704, 8144, 11532, 16164, 22480, 31056, 42568, 57972, 78480, 105610, 141336, 188208, 249352, 328824, 431760, 564468, 734992, 953424, 1232144, 1586760, 2036580, 2605352, 3322584, 4224624, 5355920

Offset: 1

Author

Jeremy Lovejoy, Jun 19 2020

Keywords

• nonn

Examples

			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) = 20.
		

Links

• S. Ahlgren, K. Bringmann, and J. Lovejoy, l-adic properties of smallest parts functions, Advances in Mathematics, 228 (2011), 629-645.
• 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.

Crossrefs

Cf. A015128, A092269, A235792, A335724, A335728.

Formula

a(n) = A335724(n) - A335728(n).

G.f.: (Product_{k>=1} (1+q^k)/(1-q^k))*(Sum_{n>=1} 2*n*q^n/(1-q^(2*n)) + Sum_{n=-oo..oo, n<>0} 4*(-1)^n*q^(n^2+n)*(1+q^(2*n)+q^(3*n))/((1-q^(2*n))*(1-q^(4*n)))).