A365666 Expansion of Sum_{0<i<j<k<l} q^(2*(i+j+k+l)-4)/( (1-q^(2*i-1))*(1-q^(2*j-1))*(1-q^(2*k-1))*(1-q^(2*l-1)) )^2.

1, 2, 4, 8, 14, 24, 40, 64, 100, 144, 212, 304, 424, 588, 800, 1072, 1422, 1864, 2408, 3080, 3950, 4972, 6224, 7760, 9564, 11742, 14344, 17384, 20968, 25204, 30112, 35840, 42548, 50078, 58888, 69048, 80474, 93628, 108608, 125408, 144536, 166224, 190348

Offset

16,2

Links

Table of n, a(n) for n=16..58.

G. E. Andrews and S. C. F. Rose, MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms, arXiv:1010.5769 [math.NT], 2010.

Formula

G.f.: (1/4) * ( Sum_{k>=4} (-1)^k * k * binomial(k+3,7) * q^(k^2) ) / ( 1 + 2 * Sum_{k>=1} (-q)^(k^2) ).

Crossrefs

A diagonal of A060047.

Cf. A002131, A002132, A060046, A365667.

Cf. A015128.

Sequence in context: A091778 A053802 A091779 * A090399 A069251 A261988

Adjacent sequences: A365663 A365664 A365665 * A365667 A365668 A365669

Keyword

nonn

Author

Seiichi Manyama, Sep 15 2023

Status

approved