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 A274789 Diagonal of the rational function 1/(1-(wxyz + wxy + wxz + wy + wz + xy + xz + y + z)). 0

%I

%S 1,9,241,9129,402321,19321689,981044401,51794295849,2814649754641,

%T 156399050208729,8845463571211521,507517525088436729,

%U 29468616564702121041,1728353228376135226329,102242911938342248555121,6093340217607472063134249,365501683327659682186607121,22049503920365906645420399769

%N Diagonal of the rational function 1/(1-(wxyz + wxy + wxz + wy + wz + xy + xz + y + z)).

%H A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil, <a href="http://arxiv.org/abs/1507.03227">Diagonals of rational functions and selected differential Galois groups</a>, arXiv:1507.03227 [math-ph], 2015.

%H Jacques-Arthur Weil, <a href="http://www.unilim.fr/pages_perso/jacques-arthur.weil/diagonals/">Supplementary Material for the Paper "Diagonals of rational functions and selected differential Galois groups"</a>

%F 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.

%t 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}];

%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Nov 16 2018 *)

%o (PARI)

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

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

%o diag(n, expr, var) = {

%o my(a = vector(n));

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

%o for (k = 1, n, a[k] = expr;

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

%o return(a);

%o };

%o diag(12, R, [x,y,z,w])

%Y Cf. A268545-A268555.

%K nonn

%O 0,2

%A _Gheorghe Coserea_, Jul 14 2016

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Last modified January 29 14:23 EST 2020. Contains 331338 sequences. (Running on oeis4.)