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A274789 Diagonal of the rational function 1/(1-(wxyz + wxy + wxz + wy + wz + xy + xz + y + z)). 0
1, 9, 241, 9129, 402321, 19321689, 981044401, 51794295849, 2814649754641, 156399050208729, 8845463571211521, 507517525088436729, 29468616564702121041, 1728353228376135226329, 102242911938342248555121, 6093340217607472063134249, 365501683327659682186607121, 22049503920365906645420399769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil, Diagonals of rational functions and selected differential Galois groups, 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+66*x^3+x^4-132*x^5+x^6+66*x^7-x^8)*y''' + (-3*x+303*x^2-396*x^3-594*x^4+405*x^5+291*x^6-6*x^7)*y'' + (-1+224*x-937*x^2+112*x^3+665*x^4+200*x^5-7*x^6)*y' + (9-169*x+254*x^2+30*x^3+5*x^4-x^5)*y, where y is g.f.

MATHEMATICA

a[n_] := SeriesCoefficient[1/(1 - (w x y z + w x y + w x z + w y + w z + x y + x z + y + z)), {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}];

Table[a[n], {n, 0, 17}] (* Jean-Fran├žois Alcover, Nov 16 2018 *)

PROG

(PARI)

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

R = 1/(1-(w*x*y*z+w*x*y+w*x*z+w*y+w*z+x*y+x*z+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: A211052 A085799 A278858 * A263158 A183903 A251670

Adjacent sequences:  A274786 A274787 A274788 * A274790 A274791 A274792

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jul 14 2016

STATUS

approved

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)