A341306 Fourier coefficients of the modular form F_{3A}^8.

1, 48, 1008, 12144, 92784, 473760, 1706544, 4818048, 12317040, 29078832, 59093280, 114031296, 219429552, 367093536, 621859968, 1037221920, 1583864688, 2403178848, 3747390192, 5232056640, 7550261280, 10938344064, 14714951616, 19930041216, 28075097520, 35731471440

Offset: 0

Author

N. J. A. Sloane, Feb 14 2021

Keywords

• nonn

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• Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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. A008655.

Programs

Maple

A341306 := proc(n)
    add( A004016(i)*x^i,i=0..n) ;
    coeftayl(%^8,x=0,n) ;
end proc:
seq(A341306(n),n=0..25) ; # R. J. Mathar, Feb 22 2021

Mathematica

A004016[n_] := If[n == 0, 1, 6 Sum[KroneckerSymbol[d, 3], {d, Divisors[n]}]];
a[n_] := SeriesCoefficient[Sum[A004016[i]*x^i, {i, 0, n}]^8, {x, 0, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 16 2023, after R. J. Mathar *)

Extensions

Terms a(5) and beyond from R. J. Mathar, Feb 22 2021