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A275045 Diagonal of the rational function 1/(1-(wxyz + wy + wz + x + y + z)). 1
1, 13, 589, 37501, 2776861, 224127793, 19128964429, 1697822272957, 155124241235293, 14493082279323913, 1378280656022778289, 132975844343348756257, 12983655880217911846621, 1280541892692200972993809, 127387054518359023378891069, 12766850683487700784950948541, 1287829822333113383109436556893 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..33

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

0 = (-x^2+108*x^3+330*x^4-4*x^5-441*x^6+12*x^7-4*x^8)*y''' + (-3*x+498*x^2+660*x^3-1350*x^4-1281*x^5+42*x^6-24*x^7)*y'' + (-1+366*x-795*x^2-1168*x^3-330*x^4+12*x^5-28*x^6)*y' + (13-215*x+208*x^2+2*x^3-4*x^4-4*x^5)*y, where y is g.f.

PROG

(PARI)

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

R = 1/(1-(w*x*y*z+w*y+w*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(12, R, [x, y, z, w])

CROSSREFS

Cf. A268545-A268555.

Sequence in context: A142210 A109875 A258303 * A296951 A067407 A143734

Adjacent sequences:  A275042 A275043 A275044 * A275046 A275047 A275048

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jul 15 2016

STATUS

approved

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Last modified July 24 11:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)