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%I #17 Sep 08 2022 08:45:29
%S 1,-4,4,0,-48,-960,-20160,-483840,-13305600,-415134720,-14529715200,
%T -564583219200,-24135932620800,-1126343522304000,-56992982228582400,
%U -3108708121559040000,-181859425111203840000,-11359219476176732160000,-754576722346025779200000
%N Expansion of e.g.f.: (1-2*x)*sqrt(1-4*x).
%F a(n) ~ -2^(2*n-3/2)*n^(n-1)/exp(n). - _Vaclav Kotesovec_, Jun 02 2013
%F D-finite with recurrence: a(n) -4*n*a(n-1) +12*(2*n-7)*a(n-2)=0. - _R. J. Mathar_, Jan 24 2020
%F Conjecture D-finite with recurrence: (-n+4)*a(n) +2*(2*n-5)*(n-3)*a(n-1)=0. - _R. J. Mathar_, Jan 24 2020
%t CoefficientList[Series[(1-2*x)*Sqrt[1-4*x], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 02 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-2*x)*Sqrt(1-4*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _Vincenzo Librandi_, Jan 25 2020
%o (PARI) seq(n)={Vec(serlaplace((1-2*x)*sqrt(1-4*x + O(x*x^n))))} \\ _Andrew Howroyd_, Jan 25 2020
%Y Cf. A126967, A126079.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Mar 22 2007
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