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A341569
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Fourier coefficients of the modular form (1/t_{6a}) * (1-12*sqrt(-3)/t_{6a})^(11/6) * F_{6a}^14.
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0
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1, 63, 1782, 29768, 324729, 2412828, 12353726, 43222410, 101978514, 169305668, 242060472, 255399480, -312214577, -1325964249, -1359793170, -4343321920, -6825676572, 5096933424, -6418882378, 3032329410, 38788733898, 13636370492, -10673080506, 132884783280, -67901221287
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OFFSET
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0,2
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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 30 2023
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LINKS
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PROG
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(Sage)
def a(n):
if n==0: return 1
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*(phi02^2 - phi12^2)*(phi02^2 + 3*phi12^2)^5)/2
return f.taylor(x, 0, n+1).coefficient(x^(n+1/2)) # Robin Visser, Jul 30 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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