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A276013
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Diagonal of (1 - 9 x y) / ((1 - 3 y - 2 x + 3 y^2 + 8 x^2 y) * (1 - u - z) * (1 - v - w)).
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1
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1, 12, 864, 100800, 14112000, 2139830784, 338341183488, 54913641209856, 9080061146956800, 1523231914913280000, 258557709598427086848, 44324863067728222027776, 7663322563977594870300672, 1334677098876385703362560000, 233951210561895726160281600000
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OFFSET
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0,2
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COMMENTS
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"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).
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LINKS
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FORMULA
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a(n) = [(xyzuvw)^n] (1-9*x*y)/((1 - 3*y - 2*x + 3*y^2 + 8*x^2*y) * (1-u-z) * (1-v-w)).
Recurrence: (n-1)^2*n^3*(3*n - 5)*a(n) = 24*(n-1)^2*(2*n - 1)^2*(3*n - 4)*(3*n - 2)*a(n-1) - 384*(2*n - 3)^2*(2*n - 1)^2*(3*n - 5)*(3*n - 2)*a(n-2).
a(n) ~ Gamma(1/3) * 2^(6*n - 7/3) * 3^(n + 1/2) / (Pi^2 * n^(4/3)). (End)
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EXAMPLE
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1 + 12*x + 864*x^2 + 100800*x^3 + ...
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MAPLE
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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 + 9*x^2*y):
expr := (1 - 9*x*y)/(pxy * (1-u-z-u*z) * (1-v-w)):
[seq(diag_coeff(expr, i), i=0..14)];
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MATHEMATICA
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f = (1 - 9 x y)/((1 - 3y - 2x + 3 y^2 + 8 x^2 y)*(1 - u - z)*(1 - v - w));
a[n_] := Fold[SeriesCoefficient[#1, {#2, 0, n}] &, f, {x, y, z, u, v, w}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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