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A347207
The number of overpartitions of n whose Frobenius symbols have only positive parts in the top row.
1
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
0,3
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.
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)).
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeremy Lovejoy, Aug 23 2021
STATUS
approved