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A341561
Fourier coefficients of the modular form (1/t_{3A}) * F_{3A}^16.
2
0, 1, 54, 1269, 16804, 134406, 628398, 1311968, -1701864, -14345991, -16443324, 25426764, 11246580, 16601078, 505866816, -113853762, -1326884336, 1507092642, -3873575034, 100819028, 2685180888, 6885133920, -20849400, 10111254408, -10371867912, -412371305, -58625773596
OFFSET
0,3
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Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. Sloane wrote 2005 on the first page but the internal evidence suggests 1997.] See page 30.
FORMULA
Convolution product of 1/A030197 and A008655^4. - Georg Fischer, Mar 30 2023
PROG
(Sage)
def a(n):
if n==0: return 0
eta = x^(1/24)*product([(1 - x^k) for k in range(1, n)])
t3A = ((eta/eta(x=x^3))^12 + 27)^2/(eta/eta(x=x^3))^12
F3A = sum([rising_factorial(1/6, k)*rising_factorial(1/3, k)/
(rising_factorial(1, k)^2)*(108/t3A)^k for k in range(n)])
f = F3A^16/t3A
return f.taylor(x, 0, n).coefficients()[n-1][0] # Robin Visser, Jul 23 2023
KEYWORD
sign
AUTHOR
Robert C. Lyons, Feb 14 2021
EXTENSIONS
More terms from Georg Fischer, Mar 30 2023
STATUS
approved