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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 February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)