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A026525 a(n) = T(2*n, n), where T is given by A026519.

%I A026525 #10 Dec 21 2021 02:34:23
%S A026525 1,1,5,16,65,251,1016,4117,16913,69865,290455,1212905,5085224,
%T A026525 21389824,90226449,381519416,1616684241,6863544233,29187402749,
%U A026525 124305180842,530108333515,2263423401745,9674857844129,41396075156859,177285394355336,759895396193376,3259667597627576,13992851410449865
%N A026525 a(n) = T(2*n, n), where T is given by A026519.
%H A026525 G. C. Greubel, <a href="/A026525/b026525.txt">Table of n, a(n) for n = 0..1000</a>
%F A026525 a(n) = A026519(2*n, n).
%F A026525 a(n) = A026536(2*n, n).
%t A026525 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/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 = A026519 *)
%t A026525 a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, T[2 n, n] ];
%t A026525 Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Dec 20 2021 *)
%o A026525 (Sage)
%o A026525 @CachedFunction
%o A026525 def T(n,k): # T = A026519
%o A026525     if (k<0 or k>2*n): return 0
%o A026525     elif (k==0 or k==2*n): return 1
%o A026525     elif (k==1 or k==2*n-1): return (n+1)//2
%o A026525     elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o A026525     else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026525 [T(2*n, n) for n in (0..40)] # _G. C. Greubel_, Dec 20 2021
%Y A026525 Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026526, A026527, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.
%Y A026525 Cf. A026536.
%K A026525 nonn
%O A026525 0,3
%A A026525 _Clark Kimberling_
%E A026525 Terms a(20) onward added by _G. C. Greubel_, Dec 20 2021