A341305 -id:A341305 - cp's OEIS frontend

A341554 Fourier coefficients of the modular form sqrt(1 - 108/t_{3A}) * F_{3A}^10.

1, 6, -810, -22134, -278634, -2122524, -11039814, -43693008, -145572714, -424326378, -1083745980, -2551211640, -5663429382, -11474793708, -22397094864, -42109347204, -74498070378, -128307428244, -217704941082, -349133308872, -555058873404, -870035772336, -1308777310008

Offset: 0

Robert C. Lyons, Feb 14 2021

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Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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 29.

Cf. A004016, A030197, A341305, A341555, A341559.

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

More terms from Georg Fischer, Mar 31 2023

A341560 Fourier coefficients of the modular form (1/t_{3A}) * sqrt( 1-108/t_{3A} ) * F_{3A}^14.

Original entry on oeis.org

0, 1, -12, -729, -8048, -30210, 8748, 235088, 194880, 531441, 362520, -11182908, 5866992, 8049614, -2821056, 22023090, 63590656, -117494622, -6377292, -214061380, 243130080, -171379152, 134194896, 830555544, -142067520, -308059025, -96595368, -387420489, -1891988224

Offset: 0

Robert C. Lyons, Feb 14 2021

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Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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, A341305, A341554, A341559.

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

More terms from Georg Fischer, Mar 31 2023

A341555 Fourier coefficients of the modular form (1/t_{3A}) * sqrt(1 - 108/t_{3A}) * F_{3A}^10.

Original entry on oeis.org

0, 1, -36, -81, 784, -1314, 2916, -4480, -9792, 6561, 47304, 1476, -63504, -151522, 161280, 106434, -48896, 108162, -236196, 593084, -1030176, 362880, -53136, -969480, 793152, -226529, 5454792, -531441, -3512320, -6642522, -3831624, 7070600, 6773760, -119556, -3893832

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Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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 29.

Cf. A004016, A030197, A341305, A341554, A341560, A341562.

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

More terms from Georg Fischer, Mar 31 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

N. J. A. Sloane, Feb 13 2021

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This is the form (1/t_{4a}) * ( 1-16*i/t_{4a} )*F_{4a}^8. Here, F_{4a} is the hypergeometric function F(1/4, 1/2; 1; 32*i/t_{4a}).

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. I wrote 2005 on the first page but the internal evidence suggests 1997.] See page 29.

Cf. A341305, A341306.

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

More terms from Robin Visser, Jul 23 2023

cp's OEIS Frontend

A341554 Fourier coefficients of the modular form sqrt(1 - 108/t_{3A}) * F_{3A}^10.

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A341560 Fourier coefficients of the modular form (1/t_{3A}) * sqrt( 1-108/t_{3A} ) * F_{3A}^14.

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A341555 Fourier coefficients of the modular form (1/t_{3A}) * sqrt(1 - 108/t_{3A}) * F_{3A}^10.

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A341304 Fourier coefficients of a modular form studied by Koike.

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