%I #10 Aug 01 2023 08:08:17
%S 0,1,3,-855,-19719,-189663,-809226,-255339,9868542,24108075,-19076611,
%T -83250516,-178059060,-774131094,1654990113,4979928843,-8282963151,
%U 7132715646,-6849297108,-29601661516,-8702922246,87845108229,5032903977,141218051814,-264089426616,302320735992,-825532125819
%N Fourier coefficients of the modular form (1/t_{6a}^3) * (1-6*sqrt(-3)/t_{6a}) * (1-12*sqrt(-3)/t_{6a})^(4/3) * F_{6a}^20.
%C Here, F_{6a} is the hypergeometric function F(1/3, 1/2; 1; 12*sqrt(-3)/t_{6a}). The definition given on page 23 in the linked manuscript has a minor typo where "t_{3A}" should be "t_{6a}". - _Robin Visser_, Jul 31 2023
%H Masao Koike, <a href="/A004016/a004016.pdf">Modular forms on non-compact arithmetic triangle groups</a>, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. Sloane wrote 2005 on the first page but the internal evidence suggests 1997.] See page 31.
%o (Sage)
%o def a(n):
%o if n==0: return 0
%o theta2 = sum([1]+[2*x^(k^2/2) for k in range(1, n+1)])
%o theta3 = sum([2*x^((k^2 + k + 1/4)/2) for k in range(n)])
%o phix = theta2(x=x^4)*theta2(x=x^12) + theta3(x=x^4)*theta3(x=x^12)
%o phiy = theta2(x=x^4)*theta3(x=x^12) + theta3(x=x^4)*theta2(x=x^12)
%o f = (phiy^3*(phix^2-phiy^2)^3*phix*(phix^2-9*phiy^2)*(phix^2+3*phiy^2)^4)/8
%o return f.taylor(x, 0, n+1).coefficient(x^(n+1/2)) # _Robin Visser_, Jul 31 2023
%K sign
%O 0,3
%A _Robert C. Lyons_, Feb 15 2021
%E More terms from _Robin Visser_, Jul 31 2023