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A274665
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Diagonal of the rational function 1/(1 - x - y - z + x*y + x*z - y*z).
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1
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1, 4, 30, 280, 2890, 31584, 358176, 4168560, 49455450, 595480600, 7254787540, 89234708160, 1106335812400, 13808393670400, 173332340911200, 2186551157230560, 27701981424940890, 352297514508697800, 4495418315974868700, 57535568476437651600, 738373616359119126540
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OFFSET
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0,2
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COMMENTS
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Annihilating differential operator: (-2*x+29*x^2-27*x^3)*Dx^2 + (-2+58*x-81*x^2)*Dx + 8-24*x.
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LINKS
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FORMULA
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G.f.: hypergeom([1/12, 5/12],[1],3456*x^5*(1-31/2*x+28*x^2-27/2*x^3)/(1-16*x+40*x^2)^3)/(1-16*x+40*x^2)^(1/4).
0 = (-2*x+29*x^2-27*x^3)*y'' + (-2+58*x-81*x^2)*y' + (8-24*x)*y, where y is the g.f.
Recurrence: 2*n^2*a(n) = (29*n^2 - 29*n + 8)*a(n-1) - 3*(3*n - 4)*(3*n - 2)*a(n-2). - Vaclav Kotesovec, Jul 05 2016
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MATHEMATICA
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a[0] = 1; a[1] = 4; a[n_] := a[n] = ((29*n^2 - 29*n + 8)*a[n-1] - 3*(3*n - 4)*(3*n - 2)*a[n-2])/(2*n^2);
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PROG
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(PARI)
my(x='x, y='y, z='z);
R = 1/(1 - x - y - 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(10, R, [x, y, z])
(PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
read("hypergeom.gpi");
N = 21; x = 'x + O('x^N);
Vec(hypergeom([1/12, 5/12], [1], 3456*x^5*(1-31/2*x+28*x^2-27/2*x^3)/(1-16*x+40*x^2)^3, N)/(1-16*x+40*x^2)^(1/4))
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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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