A275458 G.f.: 3F2([4/9, 5/9, 7/9], [2/3, 1], 729 x).

1, 210, 91728, 48348300, 27795877200, 16801416515520, 10492649333712000, 6704867164952174400, 4357981459741604877000, 2869985317222538272758000, 1909866367099566641482516800, 1281775836140482143996826609500, 866321769175062822028788514251300, 589012467640059218480339437176228000

Offset: 0

Author

Gheorghe Coserea, Jul 31 2016

Keywords

• nonn

Comments

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

Examples

			1 + 210*x + 91728*x^2 + 48348300*x^3 + ...
		

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.

Crossrefs

Cf. A268545-A268555, A275051-A275054.

Programs

Mathematica

HypergeometricPFQ[{4/9, 5/9, 7/9}, {2/3, 1}, 729 x] + O[x]^14 // CoefficientList[#, x]& (* Jean-François Alcover, Oct 23 2018 *)

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, 7/9], [2/3, 1], 729*x, N))

Formula

G.f.: hypergeom([4/9, 5/9, 7/9], [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-2)*a(n-1)=0. - R. J. Mathar, Jul 27 2022

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