A275459 G.f.: 3F2([4/9, 5/9, 8/9], [2/3, 1], 729 x).

1, 240, 111384, 61056996, 36134640360, 22349791271808, 14226080375707200, 9239577908667986880, 6091267058935364926620, 4062233028933305475849600, 2733980882372812975378956480, 1853783080629966591378982417800, 1264747920529034302126861656883140, 867379957865303554725274256161714560

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

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

Cf. A268545-A268555, A275051-A275054.

Sequence in context: A218514 A270054 A213696 * A035281 A008696 A047806

Adjacent sequences: A275456 A275457 A275458 * A275460 A275461 A275462

Keyword

nonn

Author

Gheorghe Coserea, Jul 31 2016

Status

approved