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A341304
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Fourier coefficients of a modular form studied by Koike.
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0
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1, -84, -82, -456, 4869, -2524, -10778, 6888, -11150, 4124, 38304, 81704, -71401, -225288, 99798, -40480, 212016, 37392, -419442, 905352, 141402, -690428, -399258, -682032, -615607, 936600, 1813118, 206968, -346416, -966028, 1887670, -2220264, 883796, 2965868
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OFFSET
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0,2
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COMMENTS
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This is the form (1/t_{4a}) * ( 1-16*i/t_{4a} )*F_{4a}^8. Here, F_{4a} is the hypergeometric function F(1/4, 1/2; 1; 32*i/t_{4a}).
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LINKS
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PROG
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(Sage)
def a(n):
eta = x^(1/24)*product([(1 - x^k) for k in range(1, 2*n+1)])
t4a = ((eta/eta(x=x^2))^12 - 64*(eta(x=x^2)/eta)^12) + 16*sqrt(-1)
F4a = sum([rising_factorial(1/4, k)*rising_factorial(1/2, k)/
(rising_factorial(1, k)^2)*((32*sqrt(-1))/t4a)^k for k in range(2*n+1)])
f = (1/t4a)*(1 - 16*sqrt(-1)/t4a)*(F4a^8)
return f.taylor(x, 0, n+1).coefficients()[n][0] # Robin Visser, Jul 23 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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