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.

A374929 Expansion of Sum_{1<=i<=j} q^(i+j)/( (1-q^i)*(1-q^j) )^2.

This page as a plain text file.
%I A374929 #15 Jul 24 2024 13:22:28
%S A374929 1,5,14,29,55,86,140,191,285,355,511,595,818,938,1240,1356,1810,1905,
%T A374929 2471,2640,3297,3410,4415,4399,5495,5690,6930,6895,8718,8440,10416,
%U A374929 10480,12438,12220,15295,14421,17435,17402,20595,19670,24272,22715,27433,26939,31110,29716,36735,33714,40180,39210
%N A374929 Expansion of Sum_{1<=i<=j} q^(i+j)/( (1-q^i)*(1-q^j) )^2.
%H A374929 Tewodros Amdeberhan, George E. Andrews and Roberto Tauraso, <a href="https://arxiv.org/abs/2309.03191">Extensions of MacMahon's sums of divisors</a>, arXiv:2309.03191v1 [math.CO], Sep 06 2023.
%F A374929 a(n) = (7*sigma_3(n) - (6*n+1)*sigma(n))/24.
%t A374929 A374929[n_] := (7*DivisorSigma[3, n] - (6*n + 1)*DivisorSigma[1, n])/24;
%t A374929 Array[A374929, 50, 2] (* _Paolo Xausa_, Jul 24 2024 *)
%o A374929 (PARI) a(n) = (7*sigma(n, 3)-(6*n+1)*sigma(n))/24;
%Y A374929 Cf. A374930, A374931.
%Y A374929 Cf. A000203, A001158, A002127.
%K A374929 nonn
%O A374929 2,2
%A A374929 _Seiichi Manyama_, Jul 24 2024