cp's OEIS Frontend

A275455 G.f.: 3F2([1/9, 5/9, 8/9], [1/3, 1], 729 x).

%I A275455 #15 Jul 27 2022 05:58:56
%S A275455 1,120,53550,28973100,17036182800,10496595041856,6664244456261700,
%T A275455 4320449008019199000,2844426519643185378000,1894935877560218667820800,
%U A275455 1274265873172890987907535424,863426385292565961502380501120,588738285265666300220495724048000,403569219885941102398195162309056000
%N A275455 G.f.: 3F2([1/9, 5/9, 8/9], [1/3, 1], 729 x).
%C A275455 "Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).
%H A275455 Gheorghe Coserea, <a href="/A275455/b275455.txt">Table of n, a(n) for n = 0..300</a>
%H A275455 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 A275455 G.f.: hypergeom([1/9, 5/9, 8/9], [1/3, 1], 729*x).
%F A275455 a(n) = (729^n*Gamma(1/3)*Gamma(1/9+n)*Gamma(5/9+n)*Gamma(8/9+n)*sin(Pi/9)) / (Pi*n!^2*Gamma(5/9)*Gamma(1/3+n)). - _Benedict W. J. Irwin_, Aug 10 2016
%F A275455 a(n) ~ 2*sin(Pi/9)*3^(6*n-1/2) / (Gamma(2/3)*Gamma(5/9)*n^(7/9)). - _Vaclav Kotesovec_, Aug 13 2016
%F A275455 D-finite with recurrence n^2*(3*n-2)*a(n) -3*(9*n-4)*(9*n-8)*(9*n-1)*a(n-1)=0. - _R. J. Mathar_, Jul 27 2022
%e A275455 1 + 120*x + 53550*x^2 + 28973100*x^3 + ...
%t A275455 FullSimplify[Table[(729^n Gamma[1/3]Gamma[1/9+n]Gamma[5/9+n]Gamma[8/9+n]Sin[Pi/9])/(Pi n!^2Gamma[5/9]Gamma[1/3+n]), {n, 0, 20}]] (* _Benedict W. J. Irwin_, Aug 10 2016 *)
%t A275455 CoefficientList[Series[HypergeometricPFQ[{1/9, 5/9, 8/9}, {1/3, 1}, 729*x], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Aug 13 2016 *)
%o A275455 (PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
%o A275455 read("hypergeom.gpi");
%o A275455 N = 12; x = 'x + O('x^N);
%o A275455 Vec(hypergeom([1/9, 5/9, 8/9], [1/3, 1], 729*x, N))
%Y A275455 Cf. A268545-A268555, A275051-A275054.
%K A275455 nonn
%O A275455 0,2
%A A275455 _Gheorghe Coserea_, Jul 31 2016