A275045 Diagonal of the rational function 1/(1-(wxyz + wy + wz + x + y + z)).

1, 13, 589, 37501, 2776861, 224127793, 19128964429, 1697822272957, 155124241235293, 14493082279323913, 1378280656022778289, 132975844343348756257, 12983655880217911846621, 1280541892692200972993809, 127387054518359023378891069, 12766850683487700784950948541, 1287829822333113383109436556893

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..488 (terms 0..33 from Gheorghe Coserea)

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.

Recurrence: n^3*(3*n - 7)*(3*n - 5)*(3*n - 4)*a(n) = (3*n - 7)*(3*n - 2)*(336*n^4 - 1288*n^3 + 1638*n^2 - 783*n + 123)*a(n-1) - 3*(3*n - 5)*(342*n^5 - 2280*n^4 + 5579*n^3 - 6102*n^2 + 2891*n - 466)*a(n-2) + 2*(3*n - 1)*(18*n^5 - 171*n^4 + 622*n^3 - 1062*n^2 + 825*n - 222)*a(n-3) - (n-3)^3*(3*n - 4)*(3*n - 2)*(3*n - 1)*a(n-4). - Vaclav Kotesovec, Mar 20 2023

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 A362862 A351507

Adjacent sequences: A275042 A275043 A275044 * A275046 A275047 A275048

Keyword

nonn

Author

Gheorghe Coserea, Jul 15 2016

Status

approved