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A026771 a(n) = T(2n,n-1), T given by A026769.

%I A026771 #8 Nov 01 2019 03:43:36
%S A026771 1,6,31,156,784,3962,20173,103522,535294,2787700,14613710,77072816,
%T A026771 408737760,2178631156,11666175215,62734622764,338660977020,
%U A026771 1834690352066,9971834477972,54361287536706,297170702049966,1628670524735842
%N A026771 a(n) = T(2n,n-1), T given by A026769.
%H A026771 G. C. Greubel, <a href="/A026771/b026771.txt">Table of n, a(n) for n = 1..500</a>
%p A026771 T:= proc(n,k) option remember;
%p A026771    if n<0 then 0;
%p A026771    elif k=0 or k=n then 1;
%p A026771    elif n=2 and k=1 then 2;
%p A026771    elif k <= (n-1)/2 then
%p A026771         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026771    else
%p A026771        procname(n-1,k-1)+procname(n-1,k) ;
%p A026771    end if ;
%p A026771 end proc;
%p A026771 seq(T(2*n, n-1), n=1..30); # _G. C. Greubel_, Nov 01 2019
%t A026771 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[k<=(n-1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]]; Table[T[2*n, n-1], {n, 30}] (* _G. C. Greubel_, Nov 01 2019 *)
%o A026771 (Sage)
%o A026771 @CachedFunction
%o A026771 def T(n, k):
%o A026771     if (k==0 or k==n): return 1
%o A026771     elif (n==2 and k==1): return 2
%o A026771     elif (k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026771     else: return T(n-1,k-1) + T(n-1,k)
%o A026771 [T(2*n, n-1) for n in (1..30)] # _G. C. Greubel_, Nov 01 2019
%Y A026771 Cf. A026769, A026770, A026772, A026773, A026774, A026775, A026776, A026777, A026778, A026779.
%K A026771 nonn
%O A026771 1,2
%A A026771 _Clark Kimberling_