A275460 G.f.: 3F2([2/9, 4/9, 7/9], [1/3, 1], 729 x).

1, 168, 72072, 37752000, 21636143100, 13053584427840, 8141901337189620, 5198083656717631680, 3376354693360163389875, 2222371681246143931063560, 1478289894198059998030179204, 991793399749992922720024531872, 670139971927397485144595595426978, 455519420546971097210713116712430400

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([2/9, 4/9, 7/9], [1/3, 1], 729*x).

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

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

Example

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

Mathematica

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

Crossrefs

Cf. A268545-A268555, A275051-A275054.

Sequence in context: A282375 A289327 A130215 * A364178 A275456 A185404

Adjacent sequences: A275457 A275458 A275459 * A275461 A275462 A275463

Keyword

nonn

Author

Gheorghe Coserea, Jul 31 2016

Status

approved