A318201 - OEIS

%I #20 Aug 21 2018 11:44:46

%S 1,1275,1641690,2198770140,3046553083980,4336768315045530,

%T 6307588582660665300,9334870668704489748840,

%U 14013762435241053769769940,21290019308561214243784932180,32671991169676632627962261307000,50573696461217634323724960067290000,78871365421150941315659866056940998000

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

%C A145494 is the convolution of A092870 and this sequence.

%H Seiichi Manyama, <a href="/A318201/b318201.txt">Table of n, a(n) for n = 0..309</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) = (6*12^n/(n!*(n+3)!)) * Product_{k=0..n-1} (12k+17)*(12k+25).

%F a(n) = 6*(12*n+1)*(12*n+5)*(12*n+13)*A092870(n)/(65*(n+1)*(n+2)*(n+3)).

%F 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

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

%Y 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).

%Y Cf. A145494.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 21 2018