login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275456 G.f.: 3F2([1/9, 7/9, 8/9], [1/3, 1], 729 x). 1
1, 168, 85680, 50388000, 31479903000, 20342022734880, 13431668094985140, 9002968680250888200, 6101557410115488321000, 4170391891453158061891200, 2869634745103513910507157888, 1985363415926004500849300108544, 1379778913200535726019164327886400, 962553011288199733460143650698784000 (list; graph; refs; listen; history; text; internal format)
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([1/9, 7/9, 8/9], [1/3, 1], 729*x).

a(n) = (729^n*Gamma(1/3)*Gamma(1/9+n)*Gamma(7/9+n)*Gamma(8/9+n)*sin(Pi/9)) / (Pi*n!^2*Gamma(7/9)*Gamma(1/3+n)). - Benedict W. J. Irwin, Aug 10 2016

a(n) ~ 2*sin(Pi/9)*3^(6*n-1/2) / (Gamma(2/3)*Gamma(7/9)*n^(5/9)). - Vaclav Kotesovec, Aug 13 2016

EXAMPLE

1 + 168*x + 85680*x^2 + 50388000*x^3 + ...

MATHEMATICA

FullSimplify[Table[(729^n Gamma[1/3]Gamma[1/9+n]Gamma[7/9+n]Gamma[8/9+n]Sin[Pi/9]) / (Pi n!^2Gamma[7/9]Gamma[1/3+n]), {n, 0, 20}]] (* Benedict W. J. Irwin, Aug 10 2016 *)

CoefficientList[Series[HypergeometricPFQ[{1/9, 7/9, 8/9}, {1/3, 1}, 729*x], {x, 0, 20}], x] (* Vaclav Kotesovec, Aug 13 2016 *)

PROG

(PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");

read("hypergeom.gpi");

N = 12; x = 'x + O('x^N);

Vec(hypergeom([1/9, 7/9, 8/9], [1/3, 1], 729*x, N))

CROSSREFS

Cf. A268545-A268555, A275051-A275054.

Sequence in context: A289327 A130215 A275460 * A185404 A146200 A159394

Adjacent sequences:  A275453 A275454 A275455 * A275457 A275458 A275459

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jul 31 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 18:37 EST 2021. Contains 349424 sequences. (Running on oeis4.)