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A026527 a(n) = T(2*n, n-2), where T is given by A026519.

%I A026527 #14 Jun 18 2025 07:32:03
%S A026527 1,3,14,55,231,952,3976,16614,69750,293557,1238952,5240599,22212645,
%T A026527 94318875,401143304,1708558480,7286677479,31113264579,132994055090,
%U A026527 569048532612,2437033824302,10445705817063,44807461337160,192342179361800,826205908069555,3551172735996756,15272395383833658
%N A026527 a(n) = T(2*n, n-2), where T is given by A026519.
%H A026527 G. C. Greubel, <a href="/A026527/b026527.txt">Table of n, a(n) for n = 2..1000</a>
%F A026527 a(n) = A026519(2*n, n-2).
%F A026527 a(n) = A026536(2*n, n-2).
%t A026527 T[n_, k_]:= T[n, k]= 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 A026527 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n, n-2] ];
%t A026527 Table[a[n], {n,2,40}] (* _G. C. Greubel_, Dec 20 2021 *)
%o A026527 (Sage)
%o A026527 @CachedFunction
%o A026527 def T(n,k): # T = A026552
%o A026527     if (k==0 or k==2*n): return 1
%o A026527     elif (k==1 or k==2*n-1): return (n+1)//2
%o A026527     elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o A026527     else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026527 [T(2*n,n-2) for n in (2..40)] # _G. C. Greubel_, Dec 20 2021
%Y A026527 Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.
%Y A026527 Cf. A026536.
%K A026527 nonn
%O A026527 2,2
%A A026527 _Clark Kimberling_
%E A026527 Terms a(20) onward added by _G. C. Greubel_, Dec 20 2021