login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274672 Diagonal of the rational function 1 / (1 - x - y - z - x y - y z + x y z). 1
1, 9, 211, 6093, 194211, 6552759, 229425631, 8244126669, 302001325987, 11228376095379, 422418832551981, 16044756006730779, 614293828071090831, 23677157141279202843, 917844665558530089591, 35756691970868828784813, 1399009670335978828299747, 54945874078445147692928043 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Annihilating differential operator: x*(x+2)*(8*x^2-x-6)*(2*x^3-29*x^2-41*x+1)*Dx^2 + (48*x^6-408*x^5-777*x^4+798*x^3+1847*x^2+972*x-12)*Dx + 16*x^5-52*x^4+141*x^3+529*x^2+408*x+108

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..310

A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil, Diagonals of rational functions and selected differential Galois groups, arXiv preprint arXiv:1507.03227 [math-ph], 2015.

Jacques-Arthur Weil, Supplementary Material for the Paper "Diagonals of rational functions and selected differential Galois groups"

FORMULA

G.f.: hypergeom([1/12, 5/12],[1],1728*x^3*(2*x^3-29*x^2-41*x+1)*(x+2)^2/(1-36*x-34*x^2-12*x^3+x^4)^3)/(1-36*x-34*x^2-12*x^3+x^4)^(1/4).

0 = x*(x+2)*(8*x^2-x-6)*(2*x^3-29*x^2-41*x+1)*y'' + (48*x^6-408*x^5-777*x^4+798*x^3+1847*x^2+972*x-12)*y' + (16*x^5-52*x^4+141*x^3+529*x^2+408*x+108)*y, where y is the g.f.

MATHEMATICA

gf = Hypergeometric2F1[1/12, 5/12, 1, 1728*x^3*(2*x^3 - 29*x^2 - 41*x + 1)*(x + 2)^2/(1 - 36*x - 34*x^2 - 12*x^3 + x^4)^3]/(1 - 36*x - 34*x^2 - 12*x^3 + x^4)^(1/4);

CoefficientList[gf + O[x]^20, x] (* Jean-Fran├žois Alcover, Dec 01 2017 *)

PROG

(PARI)

my(x='x, y='y, z='z);

R = 1 / (1 - x - y - z - x*y - y*z + x*y*z);

diag(n, expr, var) = {

  my(a = vector(n));

  for (i = 1, #var, expr = taylor(expr, var[#var - i + 1], n));

  for (k = 1, n, a[k] = expr;

       for (i = 1, #var, a[k] = polcoeff(a[k], k-1)));

  return(a);

};

diag(10, R, [x, y, z])

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

read("hypergeom.gpi");

N = 20; x = 'x + O('x^N);

Vec(hypergeom([1/12, 5/12], [1], 1728*x^3*(2*x^3-29*x^2-41*x+1)*(x+2)^2/(1-36*x-34*x^2-12*x^3+x^4)^3, N)/(1-36*x-34*x^2-12*x^3+x^4)^(1/4))

CROSSREFS

Cf. A268545-A268555.

Sequence in context: A218887 A001535 A300136 * A122399 A320096 A188409

Adjacent sequences:  A274669 A274670 A274671 * A274673 A274674 A274675

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jul 05 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 April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)