%I A104455
%S A104455 1,4,17,77,371,1890,10095,56040,320795,1881524,11250827,68330773,
%T A104455 420314629,2612922694,16389162537,103587298965,659071002195,
%U A104455 4217699773140,27129590096595,175303621195647,1137400502295081
%N A104455 Expansion of exp(5x)*(BesselI(0,2x)-BesselI(1,2x)).
%C A104455 Third binomial transform of A000108. In general, the k-th binomial transform 
               of A000108 will have g.f. (1-sqrt((1-(k+4)x)/(1-kx)))/(2x), e.g.f. 
               exp((k+2)x)(BesselI(0,2x)-BesselI(1,2x)) and a(n)=sum{i=0..n, C(n,
               i)C(i)k^(n-i)}.
%C A104455 Hankel transform of this sequence gives A000012 = [1,1,1,1,1,1,1,...] 
               . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 24 2007
%F A104455 G.f.: (1-sqrt((1-7x)/(1-3x)))/(2x); a(n)=sum{k=0..n, C(n, k)C(k)3^(n-k)}.
%Y A104455 Cf. A007317, A064613.
%Y A104455 Sequence in context: A081922 A124325 A151248 this_sequence A123952 A005494 
               A053486
%Y A104455 Adjacent sequences: A104452 A104453 A104454 this_sequence A104456 A104457 
               A104458
%K A104455 easy,nonn
%O A104455 0,2
%A A104455 Paul Barry (pbarry(AT)wit.ie), Mar 08 2005