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

0,3

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

Table of n, a(n) for n=0..48.

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

Crossrefs

Cf. A015128, A143184, A347207.

Sequence in context: A000011 A187213 A022476 * A307240 A000013 A064484

Adjacent sequences: A347203 A347204 A347205 * A347207 A347208 A347209

Keyword

nonn

Author

Jeremy Lovejoy, Aug 23 2021

Status

approved