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A026748 a(n) = T(2n,n), T given by A026747.

%I A026748 #11 Oct 30 2019 01:11:37
%S A026748 1,3,11,44,184,790,3452,15278,68290,307696,1395696,6367199,29193025,
%T A026748 134442102,621609060,2884432810,13428450520,62703991531,293606387095,
%U A026748 1378309455352,6485734373020,30586630485443,144544075759391,684395988590939
%N A026748 a(n) = T(2n,n), T given by A026747.
%H A026748 G. C. Greubel, <a href="/A026748/b026748.txt">Table of n, a(n) for n = 0..500</a>
%p A026748 A026747 := proc(n,k) option remember;
%p A026748    if k=0 or k = n then 1;
%p A026748    elif type(n,'even') and k <= n/2 then
%p A026748         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026748    else
%p A026748        procname(n-1,k-1)+procname(n-1,k) ;
%p A026748    end if ;
%p A026748 end proc:
%p A026748 seq(A026747(2*n,n), n=0..30); # _G. C. Greubel_, Oct 29 2019
%t A026748 T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && 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] ]]; Table[T[2n, n], {n,0,30}] (* _G. C. Greubel_, Oct 29 2019 *)
%o A026748 (Sage)
%o A026748 @CachedFunction
%o A026748 def T(n, k):
%o A026748     if (k==0 or k==n): return 1
%o A026748     elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026748     else: return T(n-1,k-1) + T(n-1,k)
%o A026748 [T(2*n, n) for n in (0..30)] # _G. C. Greubel_, Oct 29 2019
%Y A026748 Cf. A026747, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026756, A026757.
%K A026748 nonn
%O A026748 0,2
%A A026748 _Clark Kimberling_