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Expansion of Hypergeometric function F(5/12, 13/12; 2; 1728*x) in powers of x.
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%I #27 Aug 21 2018 11:44:54

%S 1,390,331500,355699500,428760177300,554472661284360,

%T 751706507941225200,1054268377387568343000,1516916483664479584186500,

%U 2226631142488300765641223800,3321243012135549422030449420080,5019605916068500831023292873530000,7670343963284674539098285610205650000

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

%C A145492 is the convolution of A092870 and this sequence.

%H Seiichi Manyama, <a href="/A318174/b318174.txt">Table of n, a(n) for n = 0..310</a>

%H M. Kaneko and D. Zagier, <a href="http://www2.math.kyushu-u.ac.jp/~mkaneko/papers/atkin.pdf">Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials</a>, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

%F a(n) = (12^n/(n!*(n+1)!)) * Product_{k=0..n-1} (12k+5)*(12k+13).

%F a(n) = (12*n+1)*A092870(n)/(n+1).

%F a(n) ~ 12^(3*n + 1) / (Gamma(1/12) * Gamma(5/12) * n^(3/2)). - _Vaclav Kotesovec_, Aug 21 2018

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

%Y 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).

%Y Cf. A145492.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 20 2018