A098560 Expansion of e.g.f. (1+4*x)/(1-4*x).

1, 8, 64, 768, 12288, 245760, 5898240, 165150720, 5284823040, 190253629440, 7610145177600, 334846387814400, 16072626615091200, 835776583984742400, 46803488703145574400, 2808209322188734464000, 179725396620079005696000

Offset: 0

Author

Paul Barry, Sep 14 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..360

Crossrefs

Cf. A098559, A098558, A032184.

Programs

Magma

[1] cat [2^(2*n+1)*Factorial(n): n in [2..30]]; // G. C. Greubel, Jan 17 2018

Mathematica

s=2;lst={1};Do[s+=n*s+s;AppendTo[lst, s], {n, 2, 5!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn=20},CoefficientList[Series[(1+4x)/(1-4x),{x,0,nn}],x] Range[0,nn]!] (* or *) Join[{1},Table[2*4^n n!,{n,20}]] (* Harvey P. Dale, Jan 16 2012 *)

PARI

for(n=0, 30, print1(if(n==0,1, 2^(2*n+1)*n!), ", ")) \\ G. C. Greubel, Jan 17 2018

Formula

a(n) = 2*4^n*n! - 0^n.

a(n+1) = 8*A034177(n).

a(n) - 4*n*a(n-1) = 0. - R. J. Mathar, Dec 21 2014

Sum_{n>=0} 1/a(n) = (exp(1/4)+1)/2. - Amiram Eldar, Feb 02 2023