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%I #12 Dec 15 2021 07:13:45
%S 0,6,26,206,1100,7314,42920,274010,1677332,10616070,66290046,
%T 419754586,2648500908,16818685050,106781976774,680250643910,
%U 4337083126232,27709045093274,177213890858938,1135003956744310,7276652578220372,46702733068082702,300013046145979184
%N a(n) = Sum_{k=0..2*n-1} T(n,k) * T(n,k+1), with T given by A026584.
%H G. C. Greubel, <a href="/A027283/b027283.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{k=0..2*n-1} A026584(n,k) * A026584(n,k+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]= Sum[T[n, k]*T[n, k+1], {k, 0, 2*n-1}];
%t Table[a[n], {n, 1, 40}] (* _G. C. Greubel_, Dec 15 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 @CachedFunction
%o def A027283(n): return sum(T(n,j)*T(n, j+1) for j in (0..2*n-1))
%o [A027283(n) for n in (1..40)] # _G. C. Greubel_, Dec 15 2021
%Y Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027284, A027285, A027286.
%K nonn
%O 1,2
%A _Clark Kimberling_
%E More terms from _Sean A. Irvine_, Oct 26 2019
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