cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A335666 a(n) is the sum, over all overpartitions of n, of the overlined parts.

This page as a plain text file.
%I A335666 #17 Jun 18 2020 03:24:46
%S A335666 1,3,10,21,46,90,168,295,511,850,1382,2198,3430,5260,7960,11861,17468,
%T A335666 25445,36670,52346,74092,103986,144840,200322,275191,375662,509816,
%U A335666 687960,923442,1233340,1639312,2168999,2857460,3748772,4898652,6377023,8271294,10690830,13771912,17683642
%N A335666 a(n) is the sum, over all overpartitions of n, of the overlined parts.
%H A335666 K. Bringmann, J. Lovejoy, and R. Osburn, <a href="https://doi.org/10.1016/j.jnt.2008.10.017">Rank and crank moments for overpartitions</a>, Journal of Number Theory, 129 (2009), 1758-1772.
%F A335666 G.f.: (Product_{k>=1} (1+q^k)/(1-q^k)) * Sum_{n>=1} n*q^n/(1+q^n).
%F A335666 a(n) = A235793(n) - A335651(n). - _Omar E. Pol_, Jun 17 2020
%e A335666 The 8 overpartitions of 8 are [3], [3'], [2,1], [2,1'], [2',1], [2',1'], [1,1,1], [1',1,1], and so a(3) = 10.
%o A335666 (PARI) my(N=44, q='q+O('q^N)); Vec( prod(k=1,N, (1+q^k)/(1-q^k)) * sum(k=1,N, k*q^k/(1+q^k)) ) \\ _Joerg Arndt_, Jun 18 2020
%Y A335666 Cf. A015128, A230441, A235790, A235792, A235793, A235798, A236000, A236001, A237047, A335651.
%Y A335666 Cf. A305101 (number of overlined parts).
%K A335666 nonn
%O A335666 1,2
%A A335666 _Jeremy Lovejoy_, Jun 17 2020