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A026590 a(n) = T(2*n, n), where T is given by A026584.

%I A026590 #12 Dec 13 2021 06:16:24
%S A026590 1,1,5,19,69,341,1203,6336,22593,121483,438533,2381512,8677763,
%T A026590 47419503,173984792,954961034,3522101709,19397198595,71831252031,
%U A026590 396646918211,1473610012405,8154682794333,30376120747792,168394714422722,628648474795879,3490216221862041,13053833414221023,72566287730964469
%N A026590 a(n) = T(2*n, n), where T is given by A026584.
%H A026590 G. C. Greubel, <a href="/A026590/b026590.txt">Table of n, a(n) for n = 0..1000</a>
%F A026590 a(n) = A026584(n, n).
%t A026590 T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
%t A026590 a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n,n]];
%t A026590 Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Dec 13 2021 *)
%o A026590 (Sage)
%o A026590 @CachedFunction
%o A026590 def T(n, k):  # T = A026584
%o A026590     if (k==0 or k==2*n): return 1
%o A026590     elif (k==1 or k==2*n-1): return (n//2)
%o A026590     else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026590 [T(2*n, n) for n in (0..40)] # _G. C. Greubel_, Dec 13 2021
%Y A026590 Cf. A026584, A026585, A026587, A026589, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
%K A026590 nonn
%O A026590 0,3
%A A026590 _Clark Kimberling_
%E A026590 Terms a(19) onward from _G. C. Greubel_, Dec 13 2021