A261035 - OEIS

%I #22 Nov 15 2024 07:00:52

%S 1,-1,-1,-1,2,-1,4,-5,7,-8,10,-15,18,-22,26,-37,46,-53,66,-84,104,

%T -122,148,-183,224,-263,312,-379,454,-531,626,-750,887,-1034,1208,

%U -1428,1672,-1936,2250,-2633,3062,-3529,4076,-4728,5460,-6264,7196,-8290,9520,-10875,12431,-14238

%N A weighted count of the number of overpartitions of n with restricted odd differences.

%C The number of overpartitions of n counted with weight (-1)^(the largest part) and such that: (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) if the smallest part of the overpartition is odd then it is overlined.

%H Vaclav Kotesovec, <a href="/A261035/b261035.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)

%H K. Bringmann, J. Dousse, J. Lovejoy, and K. Mahlburg, <a href="https://doi.org/10.37236/5248">Overpartitions with restricted odd differences</a>, Electron. J. Combin. 22 (2015), no.3, paper 3.17.

%F G.f.: Product_{n >= 1} (1+q^(3*n))/(1+q^n)^3 * (1 + 2*Sum_{n >= 1} q^(n(n+1)/2)*(1+q)^2(1+q^2)^2...(1+q^(n-1))^2*(1+q^n)/((1+q^3)(1+q^6)...(1+q^(3*n))).

%F a(n) ~ (-1)^n * exp(2*Pi*sqrt(n)/3) / (2 * 3^(3/2) * n^(3/4)). - _Vaclav Kotesovec_, Jun 12 2019

%Y Cf. A260890. Equals the convolution of A141094 and A260984.

%K sign

%O 0,5

%A _Jeremy Lovejoy_, Aug 07 2015