A341556
Fourier coefficients of the modular form F_{3A}^12.
Original entry on oeis.org
1, 72, 2376, 47592, 646344, 6305904, 45821160, 255215808, 1125009864, 4097478600, 12975540336, 37101202848, 96867424872, 232791251760, 526183909056, 1128351033648, 2286328733640, 4451427831312, 8386379869896, 15130456297056, 26613241744752, 45684436953024, 75935115663264
Offset: 0
A341561
Fourier coefficients of the modular form (1/t_{3A}) * F_{3A}^16.
Original entry on oeis.org
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
-
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
A341304
Fourier coefficients of a modular form studied by Koike.
Original entry on oeis.org
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
Offset: 0
-
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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