A365667 Expansion of Sum_{0

1, 2, 4, 8, 14, 24, 40, 64, 100, 154, 232, 332, 480, 680, 944, 1304, 1774, 2384, 3180, 4200, 5488, 7120, 9160, 11680, 14869, 18740, 23468, 29280, 36278, 44720, 54904, 67040, 81464, 98658, 118936, 142792, 170902, 203760, 242120, 286624, 338366, 398160, 467148

Offset: 25

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, A365666.

Cf. A015128.

Programs

Mathematica

nmax = 80; Drop[CoefficientList[Series[-1/5 * Sum[(-1)^k*k*Binomial[k + 4, 9]*x^(k^2), {k, 5, nmax}]/(1 + 2*Sum[(-x)^(k^2), {k, 1, nmax}]), {x, 0, nmax}], x], 25] (* Vaclav Kotesovec, Jul 30 2025 *)

Formula

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) ).