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%I #21 Oct 22 2017 23:35:22
%S 0,0,2,2,4,8,18,42,102,254,646,1670,4376,11596,31022,83670,227268,
%T 621144,1706934,4713558,13072764,36398568,101704038,285095118,
%U 801526446,2259520830,6385455594,18086805002,51339636952,146015545604
%N Expansion of 1 - x - sqrt(1 - 2*x - 3*x^2) in powers of x.
%C Except for initial terms, identical to A007971.
%H Vincenzo Librandi, <a href="/A126068/b126068.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: 1 - x - sqrt(1 - 2*x - 3*x^2). - _Michael Somos_, Jan 25 2014
%F 0 = a(n) * (9*a(n+1) + 15*a(n+2) - 12*a(n+3)) + a(n+1) * (-3*a(n+1) + 10*a(n+2) - 5*a(n+3)) + a(n+2) * (a(n+2) + a(n+3)) if n>0. - _Michael Somos_, Jan 25 2014
%F a(n) ~ 3^(n-1/2)/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Apr 20 2014
%e G.f. = 2*x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 18*x^6 + 42*x^7 + 102*x^8 + 254*x^9 + ...
%p zl:=4*(1-z+sqrt(1-2*z-3*z^2))/(1-z+sqrt(1-2*z-3*z^2))^2: gser:=series(zl, z=0, 35): seq(coeff(gser, z, n), n=-2..27);
%t a[ n_] := SeriesCoefficient[ 1 - x - Sqrt[1 - 2 x - 3 x^2], {x, 0, n}]; (* _Michael Somos_, Jan 25 2014 *)
%t CoefficientList[Series[1 - x - Sqrt[1 - 2 x - 3 x^2], {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 20 2014 *)
%o (PARI) {a(n) = polcoeff( (1 - x - sqrt(1 - 2*x - 3*x^2 + x * O(x^n))), n)}; /* _Michael Somos_, Jan 25 2014 */
%Y Cf. A007971.
%K nonn
%O 0,3
%A _Zerinvary Lajos_, Feb 28 2007
%E Better name by _Michael Somos_, Jan 25 2014
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