%I #12 Dec 15 2021 07:13:48

%S 1,2,8,40,222,1296,7770,47324,291260,1806220,11266718,70609316,

%T 444231564,2803975860,17748069294,112609964308,716010467122,

%U 4561107325336,29103104031990,185973253609716,1189979068401564,7623432519587692,48891854980251090,313874287333373820

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

%C Bisection of A026585.

%H G. C. Greubel, <a href="/A027282/b027282.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..2*n} A026584(n, k)*A026584(n, 2*n-k).

%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, 2*n-k], {k,0,2*n}];

%t Table[a[n], {n, 0, 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 A027282(n): return sum(T(n,j)*T(n, 2*n-j) for j in (0..2*n))

%o [A027282(n) for n in (0..40)] # _G. C. Greubel_, Dec 15 2021

%Y Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027283, A027284, A027285, A027286.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E More terms from _Sean A. Irvine_, Oct 26 2019