%I #9 Nov 26 2018 17:09:33

%S 1,6,39,261,1779,12288,85734,602871,4265859,30338604,216677490,

%T 1552999242,11164548078,80471658192,581340627372,4208086875915,

%U 30514467991011,221620953353844,1611867544369146

%N T(2n+1,n), array T as in A054120.

%H Robert Israel, <a href="/A052392/b052392.txt">Table of n, a(n) for n = 0..1145</a>

%F From _Robert Israel_, Nov 26 2018: (Start)

%F Empirical g.f.: (2*x^2-3*x+1)/(2*sqrt(4*x^2-8*x+1)*x)+(x-1)/(2*x).

%F Empirical recurrence: 8*n*a(n)+(-32-28*n)*a(1+n)+(78+30*n)*a(n+2)+(-45-11*n)*a(n+3)+(5+n)*a(n+4)=0. (End)

%p T:= proc(n,k) option remember;

%p if k=0 or k=n then return 1 fi;

%p if k > n then return 0 fi;

%p procname(n-1,k-1) + 2*procname(n-2,k-1) + procname(n-1,k)

%p end proc;

%p T(2,1):= 3:

%p seq(T(2*n+1,n),n=0..30); # _Robert Israel_, Nov 26 2018

%K nonn

%O 0,2

%A _Clark Kimberling_