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%I #15 Apr 27 2024 07:40:25
%S 1,210,91728,48348300,27795877200,16801416515520,10492649333712000,
%T 6704867164952174400,4357981459741604877000,2869985317222538272758000,
%U 1909866367099566641482516800,1281775836140482143996826609500,866321769175062822028788514251300,589012467640059218480339437176228000
%N G.f.: 3F2([4/9, 5/9, 7/9], [2/3, 1], 729 x).
%C "Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).
%H Gheorghe Coserea, <a href="/A275458/b275458.txt">Table of n, a(n) for n = 0..300</a>
%H A. Bostan, S. Boukraa, G. Christol, S. Hassani, J-M. Maillard <a href="http://arxiv.org/abs/1211.6031">Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity</a>, arXiv:1211.6031 [math-ph], 2012.
%F G.f.: hypergeom([4/9, 5/9, 7/9], [2/3, 1], 729*x).
%F D-finite with recurrence n^2*(3*n-1)*a(n) -3*(9*n-5)*(9*n-4)*(9*n-2)*a(n-1)=0. - _R. J. Mathar_, Jul 27 2022
%F a(n) ~ (1 + 2*cos(2*Pi/9)) * Gamma(2/9) * 3^(6*n - 1/2) / (2*Pi*Gamma(1/3) * n^(8/9)). - _Vaclav Kotesovec_, Apr 27 2024
%e 1 + 210*x + 91728*x^2 + 48348300*x^3 + ...
%t HypergeometricPFQ[{4/9, 5/9, 7/9}, {2/3, 1}, 729 x] + O[x]^14 // CoefficientList[#, x]& (* _Jean-François Alcover_, Oct 23 2018 *)
%o (PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
%o read("hypergeom.gpi");
%o N = 12; x = 'x + O('x^N);
%o Vec(hypergeom([4/9, 5/9, 7/9], [2/3, 1], 729*x, N))
%Y Cf. A268545-A268555, A275051-A275054.
%K nonn
%O 0,2
%A _Gheorghe Coserea_, Jul 31 2016
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