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E.g.f. BesselI(0,4x)+BesselI(1,4x)/2.
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%I #11 Nov 21 2013 12:48:23

%S 1,1,8,12,96,160,1280,2240,17920,32256,258048,473088,3784704,7028736,

%T 56229888,105431040,843448320,1593180160,12745441280,24216338432,

%U 193730707456,369849532416,2958796259328,5671026163712,45368209309696

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

%C Fifth binomial transform is A098665.

%H Harvey P. Dale, <a href="/A098664/b098664.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%F 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

%t 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 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Sep 20 2004