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A275048
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Diagonal of the rational function 1/(1 - 3x - 5y - 7z + xy + 2yz^2 + 3x^2z^2).
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1
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1, 616, 947175, 1812651820, 3833011883965, 8582819380142616, 19946071353510410136, 47578122531207001944168, 115702070514540009854741415, 285583642613093627090885877280, 713269435359072253352128013072035, 1798640871397075848520426334656821360, 4571867984920021228226177292547960261132
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = [(xyz)^n] 1/(1-3*x-5*y-7*z+x*y+2*y*z^2+3*x^2*z^2).
a(n) ~ c*d^n/n, where d = 2768.26905153125473648033608782909246512063674470098..., c = 0.275933667674847170980793689... . - Vaclav Kotesovec, Aug 03 2016
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MAPLE
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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
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MATHEMATICA
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m = 12;
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;
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PROG
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(PARI)
my(x='x, y='y, z='z);
R = 1/(1-3*x-5*y-7*z+x*y+2*y*z^2+3*x^2*z^2);
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(12, R, [x, y, z])
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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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