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A341572
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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.
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0
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0, 1, -21, -567, -2463, 8817, 48438, -86283, -163410, 345627, -2345707, 6501468, 1816668, -8886150, -21732951, 12436011, 28518921, 49387422, -71625060, 141851060, -257201382, -301878171, 225190881, 270088038, 1342569816, -1770304392, 1062627549, -600881166, -1830749005, -486568689
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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)])
phix = theta2(x=x^4)*theta2(x=x^12) + theta3(x=x^4)*theta3(x=x^12)
phiy = theta2(x=x^4)*theta3(x=x^12) + theta3(x=x^4)*theta2(x=x^12)
f = (phiy^3*(phix^2-phiy^2)^3*phix*(phix^2-9*phiy^2)*(phix^2+3*phiy^2)^2)/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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