A098664 E.g.f. BesselI(0,4x)+BesselI(1,4x)/2.

1, 1, 8, 12, 96, 160, 1280, 2240, 17920, 32256, 258048, 473088, 3784704, 7028736, 56229888, 105431040, 843448320, 1593180160, 12745441280, 24216338432, 193730707456, 369849532416, 2958796259328, 5671026163712, 45368209309696

Offset: 0

Author

Paul Barry, Sep 20 2004

Keywords

• easy
• nonn

Comments

Fifth binomial transform is A098665.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Programs

Mathematica

With[{nn=30},CoefficientList[Series[BesselI[0,4x]+BesselI[1,4x]/2,{x,0,nn}], x]Range[0,nn]!] (* Harvey P. Dale, May 14 2012 *)

Formula

G.f.: (1+8x-sqrt(1-16x^2))/(8xsqrt(1-16x^2));

a(n)=binomial(n, floor(n/2))4^floor(n/2).

Conjecture: (n+1)*a(n)+8(n-1)*a(n-1) -16*n*a(n-2) +128*(2-n)*a(n-3)=0. - R. J. Mathar, Dec 08 2011