A126089 Expansion of e.g.f.: (1-2*x)*sqrt(1-4*x).

1, -4, 4, 0, -48, -960, -20160, -483840, -13305600, -415134720, -14529715200, -564583219200, -24135932620800, -1126343522304000, -56992982228582400, -3108708121559040000, -181859425111203840000, -11359219476176732160000, -754576722346025779200000

Offset: 0

Author

N. J. A. Sloane, Mar 22 2007

Keywords

• sign

Crossrefs

Cf. A126967, A126079.

Programs

Magma

m:=20; R:=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

Mathematica

CoefficientList[Series[(1-2*x)*Sqrt[1-4*x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)

PARI

seq(n)={Vec(serlaplace((1-2*x)*sqrt(1-4*x + O(x*x^n))))} \\ Andrew Howroyd, Jan 25 2020

Formula

a(n) ~ -2^(2*n-3/2)*n^(n-1)/exp(n). - Vaclav Kotesovec, Jun 02 2013

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

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