OFFSET
0,2
COMMENTS
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}).
LINKS
Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.] See page 29.
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Feb 13 2021
EXTENSIONS
More terms from Robin Visser, Jul 23 2023
STATUS
approved