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A026560 a(n) = T(2*n, n-2), where T is given by A026552.

%I A026560 #10 Dec 18 2021 01:00:17
%S A026560 1,4,18,74,311,1296,5432,22796,95958,404812,1711600,7250970,30772989,
%T A026560 130810512,556867224,2373764416,10130935783,43285462884,185129287262,
%U A026560 792525473552,3395664830670,14560682746632,62482560679368,268307898599664,1152883194581155,4956738399534376,21323028570642414,91775945084805898
%N A026560 a(n) = T(2*n, n-2), where T is given by A026552.
%H A026560 G. C. Greubel, <a href="/A026560/b026560.txt">Table of n, a(n) for n = 2..1000</a>
%F A026560 a(n) = A026552(2*n, n-2).
%t A026560 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 A026560 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n, n-2]];
%t A026560 Table[a[n], {n,2,40}] (* _G. C. Greubel_, Dec 18 2021 *)
%o A026560 (Sage)
%o A026560 @CachedFunction
%o A026560 def T(n,k): # T = A026552
%o A026560     if (k==0 or k==2*n): return 1
%o A026560     elif (k==1 or k==2*n-1): return (n+2)//2
%o A026560     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026560     else: return T(n-1, k) + T(n-1, k-2)
%o A026560 [T(2*n,n-2) for n in (2..40)] # _G. C. Greubel_, Dec 18 2021
%Y A026560 Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.
%K A026560 nonn
%O A026560 2,2
%A A026560 _Clark Kimberling_
%E A026560 Terms a(20) onward from _G. C. Greubel_, Dec 18 2021