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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274668 Diagonal of the rational function 1/(1 - x - y - z - x y + x z - y z + x y z). 1
1, 7, 109, 2095, 44401, 995647, 23161909, 552919423, 13454515585, 332268466327, 8302478659069, 209447296631503, 5325782947464721, 136330694520639535, 3509805380065157989, 90806156097601965055, 2359490223343888886785, 61541525049445532797735, 1610570872210945422212365 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Annihilating differential operator: x*(5*x+4)*(x^3+19*x^2+27*x-1)*Dx^2 + (15*x^4+206*x^3+363*x^2+216*x-4)*Dx + 5*x^3+33*x^2+36*x+28.

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],13824*x^4*(1-27*x-19*x^2-x^3)/(1-28*x+54*x^2+20*x^3+x^4)^3)/(1-28*x+54*x^2+20*x^3+x^4)^(1/4).

0 = x*(5*x+4)*(x^3+19*x^2+27*x-1)*y'' + (15*x^4+206*x^3+363*x^2+216*x-4)*y' + (5*x^3+33*x^2+36*x+28)*y, where y is the g.f.

MATHEMATICA

gf = Hypergeometric2F1[1/12, 5/12, 1, 13824*x^4*(1 - 27*x - 19*x^2 - x^3) / (1 - 28*x + 54*x^2 + 20*x^3 + x^4)^3]/(1 - 28*x + 54*x^2 + 20*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 + x*z - 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 = 21; x = 'x + O('x^N);

Vec(hypergeom([1/12, 5/12], [1], 13824*x^4*(1-27*x-19*x^2-x^3)/(1-28*x+54*x^2+20*x^3+x^4)^3, N)/(1-28*x+54*x^2+20*x^3+x^4)^(1/4))

CROSSREFS

Cf. A268545-A268555.

Sequence in context: A202515 A096498 A123804 * A239848 A274787 A116875

Adjacent sequences:  A274665 A274666 A274667 * A274669 A274670 A274671

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 November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)