A341305 Fourier coefficients of the modular form (1/28)*(E_6(t)+27*E_6(3*t)).

1, -18, -594, -4878, -19026, -56268, -160974, -302544, -608850, -1185858, -1856844, -2898936, -5156046, -6683292, -9983952, -15248628, -19483218, -25557444, -39133314, -44569800, -59475276, -81989424, -95664888, -115854192, -164998350, -175837518, -220548636, -288163998, -319789008, -369200700

Offset: 0

Author

N. J. A. Sloane, Feb 13 2021

Keywords

• sign

Links

• Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.] See page 29.

Crossrefs

Cf. A013973.

Programs

Maple

A341305 := proc(n)
    local a;
    a := A013973(n);
    if modp(n,3) = 0 then
        a := a+27*A013973(n/3) ;
    end if;
    %/28 ;
end proc:
seq(A341305(n),n=0..10) ; # R. J. Mathar, Feb 22 2021

Mathematica

A013973[n_] := If[n == 0, 1, -504 DivisorSigma[5, n]];
A341305[n_] := Module[{a = A013973[n]}, If[Mod[n, 3] == 0, a = a + 27 A013973[n/3]]; a/28];
Table[A341305[n], {n, 0, 29}] (* Jean-François Alcover, Apr 30 2023, after R. J. Mathar *)