A127189 E.g.f.: sqrt((1+4*x)/(1+2*x)).

1, 1, -5, 39, -423, 5985, -105885, 2269575, -57475215, 1684565505, -56176247925, 2101511463975, -87163146984375, 3969387329933025, -196863216968342925, 10560219055989978375, -609129291476291961375, 37591662102746977850625, -2471292534125033454961125

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

D-finite with recurrence: a(n) +(6*n-7)*a(n-1) +8*(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Jan 25 2020

Mathematica

With[{nn=20}, CoefficientList[Series[Sqrt[(1 + 4 x) / (1 + 2 x)], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Jan 26 2020 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Sqrt((1+4*x)/(1+2*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // Vincenzo Librandi, Jan 26 2020

Crossrefs

Sequence in context: A317618 A024216 A380208 * A121354 A122486 A187739

Adjacent sequences: A127186 A127187 A127188 * A127190 A127191 A127192

Keyword

sign

Author

N. J. A. Sloane, Mar 26 2007

Status

approved