A365666 Expansion of Sum_{0

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

Author

Seiichi Manyama, Sep 15 2023

Keywords

• nonn

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.

Crossrefs

A diagonal of A060047.

Cf. A002131, A002132, A060046, A365667.

Cf. A015128.

Programs

Mathematica

nmax = 60; Drop[CoefficientList[Series[1/4 * Sum[(-1)^k*k*Binomial[k + 3, 7]*x^(k^2), {k, 4, nmax}]/(1 + 2*Sum[(-x)^(k^2), {k, 1, nmax}]), {x, 0, nmax}], x], 16] (* Vaclav Kotesovec, Jul 30 2025 *)

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) ).