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 A174399 Expansion of (1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2). 2
 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 G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2). D-finite with recurrence: (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 Recurrence verified using d.e. (x^5+10*x^4-5*x^3-2*x^2+x) y'' + (5*x^3-5*x^2-3*x+2) y' + 2*x^3-4*x^2+6*x-2 = 0 satisfied by the G.f. - Robert Israel, Jul 21 2019 MAPLE f:= gfun:-rectoproc({(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, a(0)=1, a(1)=-1, a(2)=1, a(3)=-2}, a(n), remember): map(f, [\$0..50]); # Robert Israel, Jul 21 2019 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 *) PROG (PARI) x='x+O('x^50); Vec((1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2)) \\ G. C. Greubel, Sep 22 2018 (Magma) m:=25; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-x^2-Sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2))); // G. C. Greubel, Sep 22 2018 CROSSREFS Sequence in context: A054917 A111419 A306768 * 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 December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)