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A027282 a(n) = self-convolution of row n of array T given by A026584.

%I A027282 #12 Dec 15 2021 07:13:48
%S A027282 1,2,8,40,222,1296,7770,47324,291260,1806220,11266718,70609316,
%T A027282 444231564,2803975860,17748069294,112609964308,716010467122,
%U A027282 4561107325336,29103104031990,185973253609716,1189979068401564,7623432519587692,48891854980251090,313874287333373820
%N A027282 a(n) = self-convolution of row n of array T given by A026584.
%C A027282 Bisection of A026585.
%H A027282 G. C. Greubel, <a href="/A027282/b027282.txt">Table of n, a(n) for n = 0..1000</a>
%F A027282 a(n) = Sum_{k=0..2*n} A026584(n, k)*A026584(n, 2*n-k).
%t A027282 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 A027282 a[n_]:= a[n]= Sum[T[n, k]*T[n, 2*n-k], {k,0,2*n}];
%t A027282 Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Dec 15 2021 *)
%o A027282 (Sage)
%o A027282 @CachedFunction
%o A027282 def T(n, k):  # T = A026584
%o A027282     if (k==0 or k==2*n): return 1
%o A027282     elif (k==1 or k==2*n-1): return (n//2)
%o A027282     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 A027282 @CachedFunction
%o A027282 def A027282(n): return sum(T(n,j)*T(n, 2*n-j) for j in (0..2*n))
%o A027282 [A027282(n) for n in (0..40)] # _G. C. Greubel_, Dec 15 2021
%Y A027282 Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027283, A027284, A027285, A027286.
%K A027282 nonn
%O A027282 0,2
%A A027282 _Clark Kimberling_
%E A027282 More terms from _Sean A. Irvine_, Oct 26 2019