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.
%I A236001 #16 Mar 01 2020 20:44:04
%S A236001 0,2,4,10,20,36,64,110,180,288,452,696,1052,1568,2304,3346,4808,6838,
%T A236001 9636,13464,18664,25684,35104,47672,64348,86368,115304,153152,202452,
%U A236001 266404,349032,455406,591856,766284,988544,1270862,1628380,2079828,2648296,3362180
%N A236001 Sum of positive ranks of all overpartitions of n.
%C A236001 Consider here that the rank of a overpartition is the largest part minus the number of parts (the same idea as the Dyson's rank of a partition).
%C A236001 It appears that the sum of all ranks of all overpartitions of n is equal to zero.
%C A236001 The equivalent sequence for partitions is A209616.
%e A236001 For n = 4 we have:
%e A236001 ---------------------------
%e A236001 Overpartitions
%e A236001 of 4 Rank
%e A236001 ---------------------------
%e A236001 4 4 - 1 = 3
%e A236001 4 4 - 1 = 3
%e A236001 2+2 2 - 2 = 0
%e A236001 2+2 2 - 2 = 0
%e A236001 3+1 3 - 2 = 1
%e A236001 3+1 3 - 2 = 1
%e A236001 3+1 3 - 2 = 1
%e A236001 3+1 3 - 2 = 1
%e A236001 2+1+1 2 - 3 = -1
%e A236001 2+1+1 2 - 3 = -1
%e A236001 2+1+1 2 - 3 = -1
%e A236001 2+1+1 2 - 3 = -1
%e A236001 1+1+1+1 1 - 4 = -3
%e A236001 1+1+1+1 1 - 4 = -3
%e A236001 ---------------------------
%e A236001 The sum of positive ranks of all overpartitions of 4 is 3+3+1+1+1+1 = 10 so a(4) = 10.
%o A236001 (PARI) a(n)={my(s=0); forpart(p=n, my(r=p[#p]-#p); if(r>0, s+=r*2^#Set(p))); s} \\ _Andrew Howroyd_, Feb 19 2020
%Y A236001 Cf. A015128, A209616, A235790, A235792, A235797, A235798, A236000.
%K A236001 nonn
%O A236001 1,2
%A A236001 _Omar E. Pol_, Jan 18 2014
%E A236001 Terms a(7) and beyond from _Andrew Howroyd_, Feb 19 2020