A347206 The number of overpartitions of n whose Frobenius symbols have only odd parts in the top row.

1, 0, 2, 2, 4, 4, 8, 10, 16, 20, 30, 38, 54, 68, 94, 120, 160, 202, 266, 334, 432, 540, 688, 856, 1080, 1334, 1668, 2052, 2542, 3110, 3828, 4660, 5698, 6906, 8394, 10130, 12250, 14720, 17716, 21210, 25412, 30310, 36172, 42994, 51114, 60558, 71740, 84732, 100052

Offset: 0

Author

Jeremy Lovejoy, Aug 23 2021

Keywords

• nonn

Comments

a(n) is also the excess of the number of overpartitions of n with an even number of non-overlined parts larger than the number of overlined parts over the number of overpartitions of n with an odd number of non-overlined parts larger than the number of overlined parts.

Links

• B. Kim, E. Kim, and J. Lovejoy, On weighted overpartitions related to some q-series in Ramanujan's lost notebook, Int. J. Number Theory 17 (2021), 603-619.

Crossrefs

Cf. A015128, A143184, A347207.

Formula

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