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A052392 T(2n+1,n), array T as in A054120.

%I A052392 #12 Apr 24 2025 08:55:32
%S A052392 1,6,39,261,1779,12288,85734,602871,4265859,30338604,216677490,
%T A052392 1552999242,11164548078,80471658192,581340627372,4208086875915,
%U A052392 30514467991011,221620953353844,1611867544369146,11738194502675910,85580528620970874,624605115244327776,4563036506245946964
%N A052392 T(2n+1,n), array T as in A054120.
%H A052392 Robert Israel, <a href="/A052392/b052392.txt">Table of n, a(n) for n = 0..1145</a>
%F A052392 From _Robert Israel_, Nov 26 2018: (Start)
%F A052392 Empirical g.f.: (2*x^2-3*x+1)/(2*sqrt(4*x^2-8*x+1)*x)+(x-1)/(2*x).
%F A052392 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 A052392 T:= proc(n,k) option remember;
%p A052392   if k=0 or k=n then return 1 fi;
%p A052392   if k > n then return 0 fi;
%p A052392   procname(n-1,k-1) + 2*procname(n-2,k-1) + procname(n-1,k)
%p A052392 end proc;
%p A052392 T(2,1):= 3:
%p A052392 seq(T(2*n+1,n),n=0..30); # _Robert Israel_, Nov 26 2018
%K A052392 nonn
%O A052392 0,2
%A A052392 _Clark Kimberling_