|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|