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 A085403 Expansion of (1-x+sqrt(1-6x+x^2))/2 in powers of x. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Series reversion of x(Sum_{k>=0} a(k)x^k) is x(Sum_{k>=0} A027307(k)x^k). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA 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 a(n) ~ -sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 20 2014 MATHEMATICA CoefficientList[Series[(1-x+Sqrt[1-6x+x^2])/2, {x, 0, 30}], x] (* Harvey P. Dale, Jun 13 2013 *) PROG (PARI) a(n)=polcoeff((1-x+sqrt(1-6*x+x^2+x*O(x^n)))/2, n) CROSSREFS A minor variation of A006318. a(n)=-A006318(n-1), n>1. Sequence in context: A202743 A007985 A097090 * A112478 A184715 A292319 Adjacent sequences:  A085400 A085401 A085402 * A085404 A085405 A085406 KEYWORD sign AUTHOR Michael Somos, Jun 28 2003 STATUS approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)