%I #12 Dec 13 2021 03:06:25
%S 1,1,8,22,121,406,2155,7624,40717,147001,792351,2892044,15703156,
%T 57728737,315180458,1164727748,6385672193,23691834033,130316812494,
%U 485018155062,2674846358141,9980763478121,55161813337474,206262229900060,1142020843590221,4277853480389546,23721423518350124,88991782850212510
%N a(n) = T(2*n-1, n-1), where T is given by A026584.
%H G. C. Greubel, <a href="/A026593/b026593.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A026584(2*n-1, n-1).
%t 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 a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n-1,n-1]];
%t Table[a[n], {n, 1, 40}] (* _G. C. Greubel_, Dec 13 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n, k): # T = A026584
%o if (k==0 or k==2*n): return 1
%o elif (k==1 or k==2*n-1): return (n//2)
%o 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 [T(2*n-1, n-1) for n in (1..40)] # _G. C. Greubel_, Dec 13 2021
%Y Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
%K nonn
%O 1,3
%A _Clark Kimberling_
%E Terms a(19) onward added by _G. C. Greubel_, Dec 13 2021