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A174399 Expansion of (1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2). 1
1, -1, 1, -2, 2, -6, 5, -21, 14, -79, 43, -308, 147, -1221, 571, -4868, 2514, -19388, 12144, -76814, 61681, -302007, 318597, -1177274, 1640389, -4553897, 8333655, -17533572, 41583474, -67607944, 203455513, -263678119, 975780382 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

G.f. A(x) satisfies A(x)=1-2x+x*A(x)+x^2*A(x)+x^2*A(x)^2.

Hankel transform is the (essentially) (1,-1) Somos-4 sequence A174400.

LINKS

Table of n, a(n) for n=0..32.

FORMULA

G.f.: (1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2).

Conjecture: (n+2)*a(n) -(2*n+1)*a(n-1) +5*(1-n)*a(n-2) +5*(2*n-5)*a(n-3) +(n-4)*a(n-4)=0. - R. J. Mathar, Sep 30 2012

MATHEMATICA

CoefficientList[Series[(1-x-x^2-Sqrt[1-2x-5x^2+10x^3+x^4])/(2x^2), {x, 0, 40}], x] (* Harvey P. Dale, Jan 28 2015 *)

CROSSREFS

Sequence in context: A201500 A054917 A111419 * A056881 A260322 A286540

Adjacent sequences:  A174396 A174397 A174398 * A174400 A174401 A174402

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 18 2010

EXTENSIONS

Corrected and extended by T. D. Noe, Apr 26 2010

STATUS

approved

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Last modified May 25 19:28 EDT 2017. Contains 287059 sequences.