A365665 Expansion of Sum_{0<i<j<k<l<m} q^(i+j+k+l+m)/( (1-q^i)*(1-q^j)*(1-q^k)*(1-q^l)*(1-q^m) )^2.

1, 3, 9, 22, 51, 108, 208, 390, 693, 1193, 1977, 3195, 4995, 7722, 11583, 17164, 24882, 35685, 50205, 70083, 96300, 131101, 176358, 235377, 310651, 407352, 529074, 682750, 874038, 1112085, 1405521, 1766259, 2206413, 2741431, 3389052, 4168089, 5103450, 6218469

Offset

15,2

Links

Table of n, a(n) for n=15..52.

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.: -(1/11) * ( Sum_{k>=5} (-1)^k * (2*k+1) * binomial(k+5,10) * q^(k*(k+1)/2) ) / ( Sum_{k>=0} (-1)^k * (2*k+1) * q^(k*(k+1)/2) ).

Crossrefs

A diagonal of A060043.

Cf. A000203, A002127, A002128, A365664.

Cf. A010816, A365631, A365667.

Sequence in context: A160462 A000711 A278668 * A160526 A121589 A227454

Adjacent sequences: A365662 A365663 A365664 * A365666 A365667 A365668

Keyword

nonn

Author

Seiichi Manyama, Sep 15 2023

Status

approved