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A026558 a(n) = T(2*n, n), where T is given by A026552.

%I A026558 #10 Dec 18 2021 01:00:08
%S A026558 1,2,7,24,93,362,1452,5880,24089,99386,412637,1721500,7211536,
%T A026558 30312960,127790379,540082784,2287577537,9707988994,41269156159,
%U A026558 175705272784,749099069183,3197651758190,13665035075871,58456775063400,250302852165368,1072680809038112,4600656305265352,19746390910296372
%N A026558 a(n) = T(2*n, n), where T is given by A026552.
%H A026558 G. C. Greubel, <a href="/A026558/b026558.txt">Table of n, a(n) for n = 0..1000</a>
%F A026558 a(n) = A026552(2*n, n).
%t A026558 T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
%t A026558 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n, n]];
%t A026558 Table[a[n], {n,0,40}] (* _G. C. Greubel_, Dec 17 2021 *)
%o A026558 (Sage)
%o A026558 @CachedFunction
%o A026558 def T(n,k): # T = A026552
%o A026558     if (k==0 or k==2*n): return 1
%o A026558     elif (k==1 or k==2*n-1): return (n+2)//2
%o A026558     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026558     else: return T(n-1, k) + T(n-1, k-2)
%o A026558 [T(2*n,n) for n in (0..40)] # _G. C. Greubel_, Dec 17 2021
%Y A026558 Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026559, A026560, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.
%K A026558 nonn
%O A026558 0,2
%A A026558 _Clark Kimberling_
%E A026558 Terms a(20) onward from _G. C. Greubel_, Dec 17 2021