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A026760 a(n) = T(2n, n-1), T given by A026758.

%I A026760 #9 Nov 01 2019 03:54:22
%S A026760 1,5,23,104,469,2119,9607,43727,199819,916631,4220267,19497608,
%T A026760 90370622,420136173,1958787580,9156770130,42912496696,201579245739,
%U A026760 949002525067,4477049676288,21162505063028,100217666089863,475421115762173
%N A026760 a(n) = T(2n, n-1), T given by A026758.
%H A026760 G. C. Greubel, <a href="/A026760/b026760.txt">Table of n, a(n) for n = 1..500</a>
%p A026760 T:= proc(n,k) option remember;
%p A026760    if n<0 then 0;
%p A026760    elif k=0 or k = n then 1;
%p A026760    elif type(n,'odd') and k <= (n-1)/2 then
%p A026760         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026760    else
%p A026760        procname(n-1,k-1)+procname(n-1,k) ;
%p A026760    end if ;
%p A026760 end proc;
%p A026760 seq(T(2*n,n-1), n=1..30); # _G. C. Greubel_, Oct 31 2019
%t A026760 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && 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, 0, 30}] (* _G. C. Greubel_, Oct 31 2019 *)
%o A026760 (Sage)
%o A026760 @CachedFunction
%o A026760 def T(n, k):
%o A026760     if (n<0): return 0
%o A026760     elif (k==0 or k==n): return 1
%o A026760     elif (mod(n,2)==1 and k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026760     else: return T(n-1,k-1) + T(n-1,k)
%o A026760 [T(2*n, n-1) for n in (1..30)] # _G. C. Greubel_, Oct 31 2019
%Y A026760 Cf. A026758, A026759, A026761, A026762, A026763, A026764, A026765, A026766, A026767, A026768.
%K A026760 nonn
%O A026760 1,2
%A A026760 _Clark Kimberling_