A318174 -id:A318174 - cp's OEIS frontend

A145492 Coefficients of certain power series associated with Atkin polynomials (see Kaneko-Zagier reference for precise definition).

1, 450, 394680, 429557700, 522037315800, 678696698599920, 923563866149496000, 1298893924326291064200, 1872892788786285985719000, 2753834730409783196154778800, 4113309164116707723917886096960

Offset: 0

N. J. A. Sloane, Feb 28 2009

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..310
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

Cf. A001421, A145493, A145494, A318174.

{a(n) = (8*n+7)*(6*n+1)!/(7*(3*n)!*n!*(n+1)!^2)} \\ Seiichi Manyama, Aug 20 2018

a(n) = (8*n+7)*(6*n+1)!/(7*(3*n)!*n!*(n+1)!^2). - Seiichi Manyama, Aug 20 2018

More terms from Vladeta Jovovic, Feb 28 2009

A318200 Expansion of Hypergeometric function F(17/12, 13/12; 3; 1728*x) in powers of x.

Original entry on oeis.org

1, 884, 961350, 1166694360, 1514952626460, 2059469884770480, 2894070055573717020, 4170217137221937001200, 6128342594004497520113460, 9149429785497381327907574160, 13838512550564789258460205917000, 21159569553888757349236649959188000, 32653750015126185895018415883446910000

Offset: 0

Seiichi Manyama, Aug 21 2018

nonn

A145493 is the convolution of A092870 and this sequence.

Seiichi Manyama, Table of n, a(n) for n = 0..309
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

F([b/2]+5/12, [(b+1)/2]+1/12; b+1; 1728*x): A092870 (b=0), A318174 (b=1), this sequence (b=2), A318201 (b=3).

Cf. A145493.

{a(n) = 2*12^n/(n!*(n+2)!)*prod(k=0, n-1, (12*k+17)*(12*k+13))}

a(n) = (2*12^n/(n!*(n+2)!)) * Product_{k=0..n-1} (12k+17)*(12k+13).
a(n) = 2*(12*n+1)*(12*n+5)*A092870(n)/(5*(n+1)*(n+2)).
a(n) ~ 2^(6*n + 5) * 3^(3*n + 2) / (5 * Gamma(1/12) * Gamma(5/12) * n^(3/2)). - Vaclav Kotesovec, Aug 21 2018

A318201 Expansion of Hypergeometric function F(17/12, 25/12; 4; 1728*x) in powers of x.

Original entry on oeis.org

1, 1275, 1641690, 2198770140, 3046553083980, 4336768315045530, 6307588582660665300, 9334870668704489748840, 14013762435241053769769940, 21290019308561214243784932180, 32671991169676632627962261307000, 50573696461217634323724960067290000, 78871365421150941315659866056940998000

Offset: 0

Seiichi Manyama, Aug 21 2018

nonn

A145494 is the convolution of A092870 and this sequence.

Seiichi Manyama, Table of n, a(n) for n = 0..309
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

F([b/2]+5/12, [(b+1)/2]+1/12; b+1; 1728*x): A092870 (b=0), A318174 (b=1), A318200 (b=2), this sequence (b=3).

Cf. A145494.

{a(n) = 6*12^n/(n!*(n+3)!)*prod(k=0, n-1, (12*k+17)*(12*k+25))}

a(n) = (6*12^n/(n!*(n+3)!)) * Product_{k=0..n-1} (12k+17)*(12k+25).
a(n) = 6*(12*n+1)*(12*n+5)*(12*n+13)*A092870(n)/(65*(n+1)*(n+2)*(n+3)).
a(n) ~ 2^(6*n + 7) * 3^(3*n + 4) / (65 * Gamma(1/12) * Gamma(5/12) * n^(3/2)). - Vaclav Kotesovec, Aug 21 2018

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A145492 Coefficients of certain power series associated with Atkin polynomials (see Kaneko-Zagier reference for precise definition).

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A318200 Expansion of Hypergeometric function F(17/12, 13/12; 3; 1728*x) in powers of x.

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A318201 Expansion of Hypergeometric function F(17/12, 25/12; 4; 1728*x) in powers of x.

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