A347207 The number of overpartitions of n whose Frobenius symbols have only positive parts in the top row.

1, 0, 2, 4, 6, 10, 16, 26, 40, 62, 92, 136, 198, 284, 404, 570, 794, 1100, 1512, 2060, 2792, 3760, 5030, 6696, 8868, 11682, 15322, 20008, 26012, 33688, 43464, 55864, 71560, 91360, 116256, 147490, 186562, 235304, 295976, 371308, 464614, 579944, 722180, 897212

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 overlined parts larger than the number of non-overlined parts over the number of overpartitions of n with an odd number of overlined parts larger than the number of non-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, A347206.

Formula

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