%I #10 Jul 31 2023 08:04:07
%S 0,1,-21,-567,-2463,8817,48438,-86283,-163410,345627,-2345707,6501468,
%T 1816668,-8886150,-21732951,12436011,28518921,49387422,-71625060,
%U 141851060,-257201382,-301878171,225190881,270088038,1342569816,-1770304392,1062627549,-600881166,-1830749005,-486568689
%N Fourier coefficients of the modular form (1/t_{6a}^3) * (1-6*sqrt(-3)/t_{6a}) * (1-12*sqrt(-3)/t_{6a})^(2/3) * F_{6a}^16.
%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, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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)^2)/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