OFFSET
0,2
COMMENTS
"Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..300
A. Bostan, S. Boukraa, G. Christol, S. Hassani, J-M. Maillard Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity, arXiv:1211.6031 [math-ph], 2012.
FORMULA
G.f.: hypergeom([4/9, 5/9, 8/9], [2/3, 1], 729*x).
D-finite with recurrence n^2*(3*n-1)*a(n) -3*(9*n-5)*(9*n-4)*(9*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022
a(n) ~ Gamma(1/9) * (1 + 2*sin(Pi/18)) * 3^(6*n - 1/2) / (2*Pi*Gamma(1/3) * n^(7/9)). - Vaclav Kotesovec, Apr 27 2024
EXAMPLE
1 + 240*x + 111384*x^2 + 61056996*x^3 + ...
MATHEMATICA
HypergeometricPFQ[{4/9, 5/9, 8/9}, {2/3, 1}, 729 x] + O[x]^14 // CoefficientList[#, x]& (* Jean-François Alcover, Oct 23 2018 *)
PROG
(PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
read("hypergeom.gpi");
N = 12; x = 'x + O('x^N);
Vec(hypergeom([4/9, 5/9, 8/9], [2/3, 1], 729*x, N))
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jul 31 2016
STATUS
approved