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A026782 a(n) = T(2n,n-1), T given by A026780.

%I A026782 #9 Nov 02 2019 19:59:54
%S A026782 1,7,40,217,1158,6150,32656,173719,926664,4958556,26619438,143365880,
%T A026782 774562478,4197344582,22810572062,124300860689,679081142350,
%U A026782 3718894341450,20412141531664,112276061739814,618806031336236,3416954495002676
%N A026782 a(n) = T(2n,n-1), T given by A026780.
%H A026782 G. C. Greubel, <a href="/A026782/b026782.txt">Table of n, a(n) for n = 1..500</a>
%p A026782 T:= proc(n,k) option remember;
%p A026782     if n<0 then 0;
%p A026782     elif k=0 or k =n then 1;
%p A026782     elif k <= n/2 then
%p A026782         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026782     else
%p A026782         procname(n-1,k-1)+procname(n-1,k) ;
%p A026782     fi ;
%p A026782 end proc:
%p A026782 seq(T(2*n,n-1), n=1..30); # _G. C. Greubel_, Nov 02 2019
%t A026782 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 A026782 Table[T[2*n, n-1], {n, 30}] (* _G. C. Greubel_, Nov 02 2019 *)
%o A026782 (Sage)
%o A026782 @CachedFunction
%o A026782 def T(n, k):
%o A026782     if (n<0): return 0
%o A026782     elif (k==0 or k==n): return 1
%o A026782     elif (k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026782     else: return T(n-1,k-1) + T(n-1,k)
%o A026782 [T(2*n, n-1) for n in (1..30)] # _G. C. Greubel_, Nov 02 2019
%Y A026782 Cf. A026780, A026781, A026783, A026784, A026785, A026786, A026787, A026788, A026789, A026790.
%K A026782 nonn
%O A026782 1,2
%A A026782 _Clark Kimberling_