%I #10 Jul 31 2023 08:04:12
%S 0,1,45,837,7971,36009,6858,-622215,-1749510,3437451,17561891,
%T -11031732,-67208940,69554250,-49492953,-261597033,1059514371,
%U -637727490,1136241540,-3548694460,1012385646,-1118737251,-2102447745,12785364702,10428178248,-5328737064,-24564279141,-20702406870
%N Fourier coefficients of the modular form (1/t_{6a}^3) * (1-12*sqrt(-3)/t_{6a})^(3/2) * F_{6a}^18.
%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, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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 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*(phi12^3*(phi02^2 - phi12^2)^3*(phi02^2 + 3*phi12^2)^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
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