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A341573
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Fourier coefficients of the modular form (1/t_{6a}^3) * (1-12*sqrt(-3)/t_{6a})^(3/2) * F_{6a}^18.
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0
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0, 1, 45, 837, 7971, 36009, 6858, -622215, -1749510, 3437451, 17561891, -11031732, -67208940, 69554250, -49492953, -261597033, 1059514371, -637727490, 1136241540, -3548694460, 1012385646, -1118737251, -2102447745, 12785364702, 10428178248, -5328737064, -24564279141, -20702406870
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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PROG
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(Sage)
def a(n):
if n==0: return 0
theta2 = sum([1]+[2*x^(k^2/2) for k in range(1, n+1)])
theta3 = sum([2*x^((k^2 + k + 1/4)/2) for k in range(n)])
phi0 = theta2(x=x^2)*theta2(x=x^6) + theta3(x=x^2)*theta3(x=x^6)
phi1 = theta2(x=x^2)*theta3(x=x^6) + theta3(x=x^2)*theta2(x=x^6)
phi02, phi12 = phi0(x=x^2), phi1(x=x^2)
f = phi0*(phi12^3*(phi02^2 - phi12^2)^3*(phi02^2 + 3*phi12^2)^4)/8
return f.taylor(x, 0, n+1).coefficient(x^(n+1/2)) # Robin Visser, Jul 31 2023
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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