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%I A275048 #20 Aug 04 2016 05:54:26
%S A275048 1,616,947175,1812651820,3833011883965,8582819380142616,
%T A275048 19946071353510410136,47578122531207001944168,
%U A275048 115702070514540009854741415,285583642613093627090885877280,713269435359072253352128013072035,1798640871397075848520426334656821360,4571867984920021228226177292547960261132
%N A275048 Diagonal of the rational function 1/(1 - 3x - 5y - 7z + xy + 2yz^2 + 3x^2z^2).
%H A275048 Gheorghe Coserea and Vaclav Kotesovec, <a href="/A275048/b275048.txt">Table of n, a(n) for n = 0..134</a> (terms 0..55 from Gheorghe Coserea)
%H A275048 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 preprint arXiv:1507.03227 [math-ph], 2015.
%H A275048 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>
%H A275048 S. Boukraa, S. Hassani, J-M. Maillard and J-A. Weil, <a href="https://arxiv.org/abs/1311.2470">Differential algebra on lattice Green functions and Calabi-Yau operators (unabridged  version)</a>, arXiv:1311.2470 [math-ph], 2013.
%F A275048 a(n) = [(xyz)^n] 1/(1-3*x-5*y-7*z+x*y+2*y*z^2+3*x^2*z^2).
%F A275048 a(n) ~ c*d^n/n, where d = 2768.26905153125473648033608782909246512063674470098..., c = 0.275933667674847170980793689... . - _Vaclav Kotesovec_, Aug 03 2016
%p A275048 a:=proc(n) 1/(1-3*x-5*y-7*z+x*y+2*y*z^2+3*x^2*z^2); coeftayl(%, x=0, n); coeftayl(%, y=0, n); coeftayl(%, z=0, n); end proc: seq(a(n), n=0..20); # _Vaclav Kotesovec_, Aug 03 2016
%t A275048 m = 12;
%t A275048 s = Series[1/(1 - 3 x - 5 y - 7 z + x  y + 2 y z^2 + 3 x^2 z^2), {x, 0, m}, {y, 0, m}, {z, 0, m}] // Normal // Expand;
%t A275048 Join[{1}, Table[Coefficient[s, (x y z)^n], {n, 1, m}]] (* _Jean-François Alcover_, Jul 26 2016 *)
%o A275048 (PARI)
%o A275048 my(x='x, y='y, z='z);
%o A275048 R = 1/(1-3*x-5*y-7*z+x*y+2*y*z^2+3*x^2*z^2);
%o A275048 diag(n, expr, var) = {
%o A275048   my(a = vector(n));
%o A275048   for (i = 1, #var, expr = taylor(expr, var[#var - i + 1], n));
%o A275048   for (k = 1, n, a[k] = expr;
%o A275048        for (i = 1, #var, a[k] = polcoeff(a[k], k-1)));
%o A275048   return(a);
%o A275048 };
%o A275048 diag(12, R, [x,y,z])
%Y A275048 Cf. A268545-A268555.
%K A275048 nonn
%O A275048 0,2
%A A275048 _Gheorghe Coserea_, Jul 19 2016

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