%I A116400
%S A116400 0,0,1,1,5,5,21,21,84,84,330,330,1287,1287,5005,5005,19448,19448,75582,
%T A116400 75582,293930,293930,1144066,1144066,4457400,4457400,17383860,17383860,
%U A116400 67863915,67863915,265182525
%N A116400 E.g.f. Bessel_I(2,2x)+Bessel_I(3,2x)+Bessel_I(4,2x).
%C A116400 T(n,2) in number triangle A116399. Double of A002054.
%F A116400 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 A116400 (PARI) a(n)=n=n\2; binomial(2*n+1,n-1)
%Y A116400 A002054(n)=a(2n)=a(2n+1).
%Y A116400 Sequence in context: A127513 A091260 A146043 this_sequence A052992 A147254 
               A007028
%Y A116400 Adjacent sequences: A116397 A116398 A116399 this_sequence A116401 A116402 
               A116403
%K A116400 easy,nonn
%O A116400 0,5
%A A116400 Paul Barry (pbarry(AT)wit.ie), Feb 13 2006