A275460 - OEIS

%I #17 Apr 27 2024 07:48:25

%S 1,168,72072,37752000,21636143100,13053584427840,8141901337189620,

%T 5198083656717631680,3376354693360163389875,2222371681246143931063560,

%U 1478289894198059998030179204,991793399749992922720024531872,670139971927397485144595595426978,455519420546971097210713116712430400

%N G.f.: 3F2([2/9, 4/9, 7/9], [1/3, 1], 729 x).

%C "Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).

%H Gheorghe Coserea, <a href="/A275460/b275460.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([2/9, 4/9, 7/9], [1/3, 1], 729*x).

%F D-finite with recurrence n^2*(3*n-2)*a(n) -3*(9*n-7)*(9*n-5)*(9*n-2)*a(n-1)=0. - _R. J. Mathar_, Jul 27 2022

%F a(n) ~ Gamma(1/3) * sin(2*Pi/9) * 3^(6*n) / (Pi * Gamma(4/9) * n^(8/9)). - _Vaclav Kotesovec_, Apr 27 2024

%e 1 + 168*x + 72072*x^2 + 37752000*x^3 + ...

%t HypergeometricPFQ[{2/9, 4/9, 7/9}, {1/3, 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([2/9, 4/9, 7/9], [1/3, 1], 729*x, N))

%Y Cf. A268545-A268555, A275051-A275054.

%K nonn

%O 0,2

%A _Gheorghe Coserea_, Jul 31 2016