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%I A341569 #10 Jul 31 2023 02:27:20
%S A341569 1,63,1782,29768,324729,2412828,12353726,43222410,101978514,169305668,
%T A341569 242060472,255399480,-312214577,-1325964249,-1359793170,-4343321920,
%U A341569 -6825676572,5096933424,-6418882378,3032329410,38788733898,13636370492,-10673080506,132884783280,-67901221287
%N A341569 Fourier coefficients of the modular form (1/t_{6a}) * (1-12*sqrt(-3)/t_{6a})^(11/6) * F_{6a}^14.
%C A341569 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 30 2023
%H A341569 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, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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 A341569 (Sage)
%o A341569 def a(n):
%o A341569     if n==0: return 1
%o A341569     theta2 = sum([1]+[2*x^(k^2/2) for k in range(1, n+1)])
%o A341569     theta3 = sum([2*x^((k^2 + k + 1/4)/2) for k in range(n)])
%o A341569     phi0 = theta2(x=x^2)*theta2(x=x^6) + theta3(x=x^2)*theta3(x=x^6)
%o A341569     phi1 = theta2(x=x^2)*theta3(x=x^6) + theta3(x=x^2)*theta2(x=x^6)
%o A341569     phi02, phi12 = phi0(x=x^2), phi1(x=x^2)
%o A341569     f = phi0*(phi12*(phi02^2 - phi12^2)*(phi02^2 + 3*phi12^2)^5)/2
%o A341569     return f.taylor(x, 0, n+1).coefficient(x^(n+1/2))  # _Robin Visser_, Jul 30 2023
%K A341569 sign
%O A341569 0,2
%A A341569 _Robert C. Lyons_, Feb 15 2021
%E A341569 More terms from _Robin Visser_, Jul 30 2023

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