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%I A026591 #11 Dec 13 2021 03:05:58
%S A026591 1,2,9,38,140,701,2534,13294,48369,258430,947694,5114572,18872399,
%T A026591 102539204,380143356,2075658454,7723000261,42330184638,157951859953,
%U A026591 868376395790,3247811317907,17899895038348,67075896452000,370442993383238,1390392820937920,7692166179956366,28910883325637649,160184255555687056
%N A026591 a(n) = T(2*n, n-1), where T is given by A026584.
%H A026591 G. C. Greubel, <a href="/A026591/b026591.txt">Table of n, a(n) for n = 1..1000</a>
%F A026591 a(n) = A026584(2*n, n-1).
%t A026591 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 A026591 a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n,n-1]];
%t A026591 Table[a[n], {n, 1, 40}] (* _G. C. Greubel_, Dec 13 2021 *)
%o A026591 (Sage)
%o A026591 @CachedFunction
%o A026591 def T(n, k): # T = A026584
%o A026591     if (k==0 or k==2*n): return 1
%o A026591     elif (k==1 or k==2*n-1): return (n//2)
%o A026591     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 A026591 [T(2*n, n-1) for n in (1..40)] # _G. C. Greubel_, Dec 13 2021
%Y A026591 Cf. A026584, A026585, A026587, A026589, A026590, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
%K A026591 nonn
%O A026591 1,2
%A A026591 _Clark Kimberling_
%E A026591 Terms a(19) onward from _G. C. Greubel_, Dec 13 2021

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