%I #2 Mar 30 2012 18:59:14
%S 0,0,1,1,5,5,21,21,84,84,330,330,1287,1287,5005,5005,19448,19448,
%T 75582,75582,293930,293930,1144066,1144066,4457400,4457400,17383860,
%U 17383860,67863915,67863915,265182525
%N E.g.f. Bessel_I(2,2x)+Bessel_I(3,2x)+Bessel_I(4,2x).
%C T(n,2) in number triangle A116399. Double of A002054.
%F G.f.: (1+x)*x^2*c(x^2)^4/(2-c(x^2)), c(x) the g.f. of A000108; a(n)=C(n+1,n/2-1)(1+(-1)^n)/2 + C(n,(n-1)/2-1)(1-(-1)^n)/2.
%o (PARI) a(n)=n=n\2; binomial(2*n+1,n-1)
%Y A002054(n)=a(2n)=a(2n+1).
%K easy,nonn
%O 0,5
%A _Paul Barry_, Feb 13 2006