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

1, 5, 14, 29, 55, 86, 140, 191, 285, 355, 511, 595, 818, 938, 1240, 1356, 1810, 1905, 2471, 2640, 3297, 3410, 4415, 4399, 5495, 5690, 6930, 6895, 8718, 8440, 10416, 10480, 12438, 12220, 15295, 14421, 17435, 17402, 20595, 19670, 24272, 22715, 27433, 26939, 31110, 29716, 36735, 33714, 40180, 39210

Offset

2,2

Links

Table of n, a(n) for n=2..51.

Tewodros Amdeberhan, George E. Andrews and Roberto Tauraso, Extensions of MacMahon's sums of divisors, arXiv:2309.03191v1 [math.CO], Sep 06 2023.

Formula

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

Mathematica

A374929[n_] := (7*DivisorSigma[3, n] - (6*n + 1)*DivisorSigma[1, n])/24;
Array[A374929, 50, 2] (* Paolo Xausa, Jul 24 2024 *)

Prog

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

Crossrefs

Cf. A374930, A374931.

Cf. A000203, A001158, A002127.

Sequence in context: A256666 A319007 A211651 * A299291 A019262 A212919

Adjacent sequences: A374926 A374927 A374928 * A374930 A374931 A374932

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2024

Status

approved