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A098334
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Expansion of 1/sqrt(1-2x+17x^2).
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6
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1, 1, -7, -23, 49, 401, 41, -5767, -11423, 65569, 299353, -441847, -5511791, -3665999, 79937417, 212712857, -861871423, -5076450239, 3966949049, 89482678313, 110424995569, -1233175514671, -4202194115863, 11830822055353, 91629438996001, -13485315511199
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OFFSET
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0,3
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COMMENTS
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Central coefficients of (1+x-4x^2)^n.
Binomial transform of 1/sqrt(1+16x^2), or (1,0,-8,0,96,0,-1280,...).
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LINKS
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FORMULA
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E.g.f.: exp(x)BesselI(0, 4*I*x), I=sqrt(-1);
a(n) = sum{k=0..floor(n/2), binomial(n, 2k)binomial(2k, k)(-4)^k};
a(n) = sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)(-4)^k);
a(n) = sum{k=0..n, binomial(n, k)binomial(k, k/2)cos(pi*k/2)2^k}3.
D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +17*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 24 2012
a(n) = hypergeom([-n/2, 1/2-n/2], [1], -16). - Peter Luschny, Sep 18 2014
a(n) = (sqrt(17))^n*P(n,1/sqrt(17)), where P(n,x) is the Legendre polynomial of degree n. - Peter Bala, Mar 18 2018
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MAPLE
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a := n -> hypergeom([-n/2, 1/2-n/2], [1], -16);
seq(round(evalf(a(n), 99)), n=0..28); # Peter Luschny, Sep 18 2014
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[1-2*x+17*x^2], {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 09 2014 *)
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PROG
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(PARI) x='x+O('x^99); Vec(1/(1-2*x+17*x^2)^(1/2)) \\ Altug Alkan, Mar 18 2018
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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