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A365664
Expansion of Sum_{0<i<j<k<l} q^(i+j+k+l)/( (1-q^i)*(1-q^j)*(1-q^k)*(1-q^l) )^2.
4
1, 3, 9, 22, 51, 97, 188, 330, 568, 918, 1452, 2233, 3344, 4884, 7004, 9856, 13653, 18699, 25080, 33462, 43918, 57304, 73668, 94482, 119262, 150285, 187231, 232560, 285660, 350746, 425627, 516477, 620731, 745503, 887796, 1056669, 1247521, 1472460, 1726054, 2021327
OFFSET
10,2
LINKS
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.: (1/9) * ( Sum_{k>=4} (-1)^k * (2*k+1) * binomial(k+4,8) * q^(k*(k+1)/2) ) / ( Sum_{k>=0} (-1)^k * (2*k+1) * q^(k*(k+1)/2) ).
a(n) = (5*sigma_7(n) - (126*n-441)*sigma_5(n) + (756*n^2-4410*n+4935)*sigma_3(n) - (840*n^3-5880*n^2+9870*n-3229)*sigma(n))/967680. - Seiichi Manyama, Jul 24 2024
PROG
(PARI) a(n) = (5*sigma(n, 7)-(126*n-441)*sigma(n, 5)+(756*n^2-4410*n+4935)*sigma(n, 3)-(840*n^3-5880*n^2+9870*n-3229)*sigma(n))/967680; \\ Seiichi Manyama, Jul 24 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 15 2023
STATUS
approved