This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275461 #15 Apr 27 2024 07:52:18 %S A275461 1,105,38808,18595500,10000998000,5742915942960,3440119256028000, %T A275461 2122455291847675200,1338358017590361495000,858192528139829777895000, %U A275461 557657055926757140695941600,366299456771890110076863664500,242765837117133913048941576656100,162109136966873437562041203714292500 %N A275461 G.f.: 3F2([2/9, 5/9, 7/9], [2/3, 1], 729 x). %C A275461 "Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link). %H A275461 Gheorghe Coserea, <a href="/A275461/b275461.txt">Table of n, a(n) for n = 0..300</a> %H A275461 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 A275461 G.f.: hypergeom([2/9, 5/9, 7/9], [2/3, 1], 729*x). %F A275461 D-finite with recurrence n^2*(3*n-1)*a(n) -3*(9*n-7)*(9*n-4)*(9*n-2)*a(n-1)=0. - _R. J. Mathar_, Jul 27 2022 %F A275461 a(n) ~ (1 + 2*cos(2*Pi/9)) * Gamma(4/9) * 3^(6*n - 1/2) / (2*Pi * Gamma(1/3) * n^(10/9)). - _Vaclav Kotesovec_, Apr 27 2024 %e A275461 1 + 105*x + 38808*x^2 + 18595500*x^3 + ... %t A275461 HypergeometricPFQ[{2/9, 5/9, 7/9}, {2/3, 1}, 729 x] + O[x]^14 // CoefficientList[#, x]& (* _Jean-François Alcover_, Oct 23 2018 *) %o A275461 (PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi"); %o A275461 read("hypergeom.gpi"); %o A275461 N = 12; x = 'x + O('x^N); %o A275461 Vec(hypergeom([2/9, 5/9, 7/9], [2/3, 1], 729*x, N)) %Y A275461 Cf. A268545-A268555, A275051-A275054. %K A275461 nonn %O A275461 0,2 %A A275461 _Gheorghe Coserea_, Jul 31 2016