A341561 Fourier coefficients of the modular form (1/t_{3A}) * F_{3A}^16.

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

Table of n, a(n) for n=0..26.

Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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

Crossrefs

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

Sequence in context: A071803 A215836 A160289 * A079876 A017770 A035722

Adjacent sequences: A341558 A341559 A341560 * A341562 A341563 A341564

Keyword

sign

Author

Robert C. Lyons, Feb 14 2021

Extensions

More terms from Georg Fischer, Mar 30 2023

Status

approved