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