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%I #10 Jul 31 2023 05:26:35
%S 1,39,630,5336,24201,48636,-9010,-130950,-28494,-536860,-1191576,
%T 2163096,-1089665,1915839,5242734,1311824,-7589916,7560720,-14913082,
%U -3150750,-14651190,8250716,-7614810,-8887536,25910649,73227294,-21473658,59100840,47646780,-125614836,-7751458
%N Fourier coefficients of the modular form (1/t_{6a}) * (1-12*sqrt(-3)/t_{6a})^(7/6) * F_{6a}^10.
%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, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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 30.
%o (Sage)
%o def a(n):
%o if n==0: return 1
%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 phi0 = theta2(x=x^2)*theta2(x=x^6) + theta3(x=x^2)*theta3(x=x^6)
%o phi1 = theta2(x=x^2)*theta3(x=x^6) + theta3(x=x^2)*theta2(x=x^6)
%o phi02, phi12 = phi0(x=x^2), phi1(x=x^2)
%o f = phi0*(phi12*(phi02^2 - phi12^2)*(phi02^2 + 3*phi12^2)^3)/2
%o return f.taylor(x, 0, n+1).coefficient(x^(n+1/2)) # _Robin Visser_, Jul 31 2023
%K sign
%O 0,2
%A _Robert C. Lyons_, Feb 15 2021
%E More terms from _Robin Visser_, Jul 31 2023
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