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A098336
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Expansion of 1/sqrt(1 - 4*x + 12*x^2).
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4
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1, 2, 0, -16, -56, -48, 384, 1920, 3168, -8512, -66560, -161280, 113920, 2224640, 7311360, 3354624, -69253632, -306754560, -408059904, 1898029056, 12054196224, 25377005568, -38874316800, -443400781824, -1289598418944
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OFFSET
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0,2
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COMMENTS
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Central coefficients of (1 + 2*x - 2*x^2)^n.
Diagonal of rational function 1/(1 - (2*x^2 + 2*x*y - y^2)). - Gheorghe Coserea, Aug 04 2018
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LINKS
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FORMULA
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E.g.f.: exp(2*x)*BesselI(0, 2*sqrt(-2)*x).
a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(n-k, k)* 2^n* (-2)^(-k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(2(n-k), k)*(-3)^k. - Paul Barry, Sep 08 2004
D-finite with recurrence: n*a(n) + 2*(-2*n+1)*a(n-1) + 12*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 24 2012
G.f.: G(0), where G(k) = 1 + 2*x*(1-3*x)*(4*k+1)/( 2*k+1 - x*(1-3*x)*(2*k+1)*(4*k+3)/(x*(1-3*x)*(4*k+3) + (k+1)/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jun 30 2013
Lim sup_{n->infinity} |a(n)|/((2*sqrt(3))^n/sqrt(Pi*n)) = 6^(1/4). - Vaclav Kotesovec, Oct 09 2013
a(n) = 2^n*hypergeom([-n/2, 1/2-n/2], [1], -2). - Peter Luschny, Sep 18 2014
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MAPLE
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A098336 := n -> 2^n*hypergeom([-n/2, 1/2-n/2], [1], -2);
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[1-4*x+12*x^2], {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 09 2013 *)
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PROG
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(PARI) Vec(1/sqrt(1-4*x+12*x^2) + O(x^50)) \\ G. C. Greubel, Jan 30 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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