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A276017 Diagonal of (1 - 9 x y)/((1 - 3 y - 2 x + 3 y^2 + 8 x^2 y) * (1 - u - v - w)). 1
1, 18, 2160, 423360, 99792000, 25499650176, 6797581959168, 1860535606026240, 518890571236477440, 146835076503772800000, 42046646730013562757120, 12160617341681775057960960, 3547136319516173918512742400, 1042325945372157283978798694400, 308269259704090665806809006080000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
"The corresponding (order-five) linear differential operator is not homomorphic to its adjoint, even with an algebraic extension, and its differential Galois group is SL(5,C)." (see A. Bostan link).
LINKS
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, Eq. (C.3).
FORMULA
a(n) = [(xyuvw)^n] (1 - 9*x*y)/((1 - 3*y - 2*x + 3*y^2 + 8*x^2*y) * (1 - u - v - w)).
From Vaclav Kotesovec, Dec 03 2017: (Start)
Recurrence: (n-1)^2*n^3*(3*n - 5)*a(n) = 18*(n-1)^2*(3*n - 4)*(3*n - 2)^2*(3*n - 1)*a(n-1) - 216*(3*n - 5)^2*(3*n - 4)*(3*n - 2)^2*(3*n - 1)*a(n-2).
a(n) ~ Gamma(1/3) * 2^(2*n - 10/3) * 3^(4*n + 1) / (Pi^2 * n^(4/3)). (End)
EXAMPLE
1 + 18*x + 2160*x^2 + 423360*x^3 + ...
MAPLE
diag_coeff := proc(expr, n)
local var := [seq(indets(expr))], nvar := numelems(var);
coeftayl(expr, var=[seq(0, i=1..nvar)], [seq(n, i=1..nvar)]);
end proc:
pxy := (1 - 3*y - 2*x + 3*y^2 + 8*x^2*y):
expr := (1 - 9*x*y)/(pxy * (1 - u - v - w)):
[seq(diag_coeff(expr, i), i=0..14)];
MATHEMATICA
f = (1 - 9 x y)/((1 - 3 y - 2 x + 3 y^2 + 8 x^2 y)*(1 - u - v - w));
a[n_] := Fold[SeriesCoefficient[#1, {#2, 0, n}]&, f, {x, y, u, v, w}];
Array[a, 40, 0] (* Jean-François Alcover, Dec 03 2017 *)
CROSSREFS
Sequence in context: A296614 A341842 A230818 * A178630 A136834 A279296
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Aug 16 2016
STATUS
approved

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)