A318201 -id:A318201 - cp's OEIS frontend

A318174 Expansion of Hypergeometric function F(5/12, 13/12; 2; 1728*x) in powers of x.

1, 390, 331500, 355699500, 428760177300, 554472661284360, 751706507941225200, 1054268377387568343000, 1516916483664479584186500, 2226631142488300765641223800, 3321243012135549422030449420080, 5019605916068500831023292873530000, 7670343963284674539098285610205650000

Offset: 0

Seiichi Manyama, Aug 20 2018

nonn

A145492 is the convolution of A092870 and this sequence.

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

F([b/2]+5/12, [(b+1)/2]+1/12; b+1; 1728*x): A092870 (b=0), this sequence (b=1), A318200 (b=2), A318201 (b=3).

Cf. A145492.

{a(n) = 12^n/(n!*(n+1)!)*prod(k=0, n-1, (12*k+5)*(12*k+13))}

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

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

cp's OEIS Frontend

A318174 Expansion of Hypergeometric function F(5/12, 13/12; 2; 1728*x) in powers of x.

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