A341561 - OEIS

%I #18 Jul 24 2023 09:23:51

%S 0,1,54,1269,16804,134406,628398,1311968,-1701864,-14345991,-16443324,

%T 25426764,11246580,16601078,505866816,-113853762,-1326884336,

%U 1507092642,-3873575034,100819028,2685180888,6885133920,-20849400,10111254408,-10371867912,-412371305,-58625773596

%N Fourier coefficients of the modular form (1/t_{3A}) * F_{3A}^16.

%H Masao Koike, <a href="/A004016/a004016.pdf">Modular forms on non-compact arithmetic triangle groups</a>, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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.

%F Convolution product of 1/A030197 and A008655^4. - _Georg Fischer_, Mar 30 2023

%o (Sage)

%o def a(n):

%o     if n==0: return 0

%o     eta = x^(1/24)*product([(1 - x^k) for k in range(1, n)])

%o     t3A = ((eta/eta(x=x^3))^12 + 27)^2/(eta/eta(x=x^3))^12

%o     F3A = sum([rising_factorial(1/6, k)*rising_factorial(1/3, k)/

%o       (rising_factorial(1,k)^2)*(108/t3A)^k for k in range(n)])

%o     f = F3A^16/t3A

%o     return f.taylor(x,0,n).coefficients()[n-1][0]  # _Robin Visser_, Jul 23 2023

%Y Cf. A004016, A008655, A030197, A136747, A341306, A341556, A341557, A341558.

%K sign

%O 0,3

%A _Robert C. Lyons_, Feb 14 2021

%E More terms from _Georg Fischer_, Mar 30 2023