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%I #10 Dec 18 2021 01:00:12
%S 1,3,12,45,180,721,2940,12069,49935,207691,867900,3640429,15319395,
%T 64643580,273431408,1158988141,4921651521,20934115963,89173404140,
%U 380355072153,1624282578215,6943928981859,29715239620368,127276313406125,545605497876400,2340694589348376,10048952593607088,43170264470594302
%N a(n) = T(2*n, n-1), where T is given by A026552.
%H G. C. Greubel, <a href="/A026559/b026559.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A026552(2*n, 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)/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=A026552 *)
%t a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n, n-1]];
%t Table[a[n], {n,40}] (* _G. C. Greubel_, Dec 17 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n,k): # T = A026552
%o if (k==0 or k==2*n): return 1
%o elif (k==1 or k==2*n-1): return (n+2)//2
%o elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o else: return T(n-1, k) + T(n-1, k-2)
%o [T(2*n,n-1) for n in (1..40)] # _G. C. Greubel_, Dec 17 2021
%Y Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026560, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Terms a(20) onward added by _G. C. Greubel_, Dec 17 2021
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