A136747 -id:A136747 - cp's OEIS frontend

A341558 Fourier coefficients of the modular form (1/t_{3A}^2) * F_{3A}^12.

0, 0, 1, -12, 54, -100, 45, -108, 692, -108, -2970, 1012, 4542, 13176, -25168, -33660, 27864, 97944, 61641, -295812, -142780, 227172, 613548, -32656, -1181916, 54000, 449990, 1389960, -1340064, -1153484, 2112750, 18684, 1743312, -6661260, 733698, 2254360, 3347622

Offset: 0

Robert C. Lyons, Feb 14 2021

sign

Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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

Cf. A004016, A030197, A136747, A341556, A341557, A341561.

1/t_{3A} is A030197, F_{3A} is A004016. - Georg Fischer, Mar 31 2023

More terms from Georg Fischer, Mar 31 2023

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

Robert C. Lyons, Feb 14 2021

sign

Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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

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

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

Convolution product of 1/A030197 and A008655^4. - Georg Fischer, Mar 30 2023

More terms from Georg Fischer, Mar 30 2023

cp's OEIS Frontend

A341558 Fourier coefficients of the modular form (1/t_{3A}^2) * F_{3A}^12.

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