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%I #10 Dec 21 2021 02:34:11
%S 1,2,8,28,111,436,1763,7176,29521,122182,508595,2126312,8923136,
%T 37563930,158563368,670893296,2844444761,12081753410,51400091942,
%U 218990735668,934228356445,3990177231742,17060699906541,73017457810032,312785412844736,1340988707637776,5753539499846507
%N a(n) = T(2*n-1, n-1), T given by A026519.
%H G. C. Greubel, <a href="/A026528/b026528.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A026519(2*n-1, n-1).
%F a(n) = A026552(2*n-1, n-1).
%t 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 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n-1, n-1] ];
%t Table[a[n], {n,40}] (* _G. C. Greubel_, Dec 20 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n,k): # T = A026519
%o if (k<0 or k>2*n): return 0
%o elif (k==0 or k==2*n): return 1
%o elif (k==1 or k==2*n-1): return (n+1)//2
%o elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o [T(2*n-1,n-1) for n in (1..40)] # _G. C. Greubel_, Dec 20 2021
%Y Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.
%Y Cf. A026552.
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Terms a(20) onward added by _G. C. Greubel_, Dec 20 2021
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