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A026783 a(n) = T(2n, n-2), T given by A026780.

%I A026783 #7 Nov 02 2019 20:00:00
%S A026783 1,11,84,557,3446,20514,119336,684227,3886460,21939528,123347842,
%T A026783 691644044,3871738018,21652138770,121026492186,676391629701,
%U A026783 3780636102222,21137831159462,118234019051048,661686074145618,3705252204960252
%N A026783 a(n) = T(2n, n-2), T given by A026780.
%H A026783 G. C. Greubel, <a href="/A026783/b026783.txt">Table of n, a(n) for n = 2..500</a>
%p A026783 T:= proc(n,k) option remember;
%p A026783     if n<0 then 0;
%p A026783     elif k=0 or k =n then 1;
%p A026783     elif k <= n/2 then
%p A026783         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026783     else
%p A026783         procname(n-1,k-1)+procname(n-1,k) ;
%p A026783     fi ;
%p A026783 end proc:
%p A026783 seq(T(2*n,n-2), n=2..30); # _G. C. Greubel_, Nov 02 2019
%t A026783 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[k<=n/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]];
%t A026783 Table[T[2*n, n-2], {n,2,30}] (* _G. C. Greubel_, Nov 02 2019 *)
%o A026783 (Sage)
%o A026783 @CachedFunction
%o A026783 def T(n, k):
%o A026783     if (n<0): return 0
%o A026783     elif (k==0 or k==n): return 1
%o A026783     elif (k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026783     else: return T(n-1,k-1) + T(n-1,k)
%o A026783 [T(2*n, n-2) for n in (2..30)] # _G. C. Greubel_, Nov 02 2019
%Y A026783 Cf. A026780, A026781, A026782, A026784, A026785, A026786, A026787, A026788, A026789, A026790.
%K A026783 nonn
%O A026783 2,2
%A A026783 _Clark Kimberling_