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Expansion of Sum_{0<i<j<k<l<m} q^(2*(i+j+k+l+m)-5)/( (1-q^(2*i-1))*(1-q^(2*j-1))*(1-q^(2*k-1))*(1-q^(2*l-1))*(1-q^(2*m-1)) )^2.
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%I #13 Sep 15 2023 10:33:06

%S 1,2,4,8,14,24,40,64,100,154,232,332,480,680,944,1304,1774,2384,3180,

%T 4200,5488,7120,9160,11680,14869,18740,23468,29280,36278,44720,54904,

%U 67040,81464,98658,118936,142792,170902,203760,242120,286624,338366,398160,467148

%N Expansion of Sum_{0<i<j<k<l<m} q^(2*(i+j+k+l+m)-5)/( (1-q^(2*i-1))*(1-q^(2*j-1))*(1-q^(2*k-1))*(1-q^(2*l-1))*(1-q^(2*m-1)) )^2.

%H G. E. Andrews and S. C. F. Rose, <a href="http://arxiv.org/abs/1010.5769">MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms</a>, arXiv:1010.5769 [math.NT], 2010.

%F G.f.: -(1/5) * ( Sum_{k>=5} (-1)^k * k * binomial(k+4,9) * q^(k^2) ) / ( 1 + 2 * Sum_{k>=1} (-q)^(k^2) ).

%Y A diagonal of A060047.

%Y Cf. A002131, A002132, A060046, A365666.

%Y Cf. A015128.

%K nonn

%O 25,2

%A _Seiichi Manyama_, Sep 15 2023