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Expansion of Sum_{1<=i<=j} q^(i+j)/( (1-q^i)*(1-q^j) )^2.
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%I #15 Jul 24 2024 13:22:28

%S 1,5,14,29,55,86,140,191,285,355,511,595,818,938,1240,1356,1810,1905,

%T 2471,2640,3297,3410,4415,4399,5495,5690,6930,6895,8718,8440,10416,

%U 10480,12438,12220,15295,14421,17435,17402,20595,19670,24272,22715,27433,26939,31110,29716,36735,33714,40180,39210

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

%H 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 a(n) = (7*sigma_3(n) - (6*n+1)*sigma(n))/24.

%t A374929[n_] := (7*DivisorSigma[3, n] - (6*n + 1)*DivisorSigma[1, n])/24;

%t Array[A374929, 50, 2] (* _Paolo Xausa_, Jul 24 2024 *)

%o (PARI) a(n) = (7*sigma(n, 3)-(6*n+1)*sigma(n))/24;

%Y Cf. A374930, A374931.

%Y Cf. A000203, A001158, A002127.

%K nonn

%O 2,2

%A _Seiichi Manyama_, Jul 24 2024