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A085403
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Expansion of (1-x+sqrt(1-6x+x^2))/2 in powers of x.
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8
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1, -2, -2, -6, -22, -90, -394, -1806, -8558, -41586, -206098, -1037718, -5293446, -27297738, -142078746, -745387038, -3937603038, -20927156706, -111818026018, -600318853926, -3236724317174, -17518619320890, -95149655201962, -518431875418926, -2832923350929742
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OFFSET
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0,2
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COMMENTS
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Series reversion of x(Sum_{k>=0} a(k)x^k) is x(Sum_{k>=0} A027307(k)x^k).
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LINKS
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Table of n, a(n) for n=0..24.
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FORMULA
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G.f.: (1-x+sqrt(1-6x+x^2))/2. (=1/g.f. A006318)
Given g.f. A(x), y=A(x)x satisfies 0=f(x, y) where f(x, y)=y(y-x)+(x+y)x^2 . - Michael Somos, May 23 2005
G.f.: Q(0) where Q(k) = 1 + k*(1-x) - x - x*(k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Mar 14 2013
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PROG
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(PARI) a(n)=polcoeff((1-x+sqrt(1-6*x+x^2+x*O(x^n)))/2, n)
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CROSSREFS
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A minor variation of A006318. a(n)=-A006318(n-1), n>1.
Sequence in context: A202743 A007985 A097090 * A112478 A184715 A138801
Adjacent sequences: A085400 A085401 A085402 * A085404 A085405 A085406
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 28 2003
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STATUS
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approved
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