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A027267 a(n) = self-convolution of row n of array T given by A026536.

%I A027267 #11 Apr 12 2022 04:23:08
%S A027267 1,2,8,26,196,692,5774,21142,180772,675344,5837908,22087716,192239854,
%T A027267 733698032,6416509142,24645099530,216309089956,834847581048,
%U A027267 7347943049432,28467646552432,251119894730596,975892708569952,8624336421678788,33600628889991916,297394187356638766
%N A027267 a(n) = self-convolution of row n of array T given by A026536.
%H A027267 G. C. Greubel, <a href="/A027267/b027267.txt">Table of n, a(n) for n = 0..500</a>
%F A027267 a(n) = Sum_{k=0..2*n} A026536(n, k)*A026536(n, 2*n-k). - _G. C. Greubel_, Apr 12 2022
%t A027267 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], T[n-1, k-2] +T[n-1, k-1] +T[n-1, k], T[n-1, k-2] +T[n-1, k]] ]];
%t A027267 Table[Sum[T[n,k]*T[n,2*n-k], {k,0,2*n}], {n,0,40}] (* _G. C. Greubel_, Apr 12 2022 *)
%o A027267 (SageMath)
%o A027267 @CachedFunction
%o A027267 def T(n, k): # A026536
%o A027267     if k < 0 or n < 0: return 0
%o A027267     elif k == 0 or k == 2*n: return 1
%o A027267     elif k == 1 or k == 2*n-1: return n//2
%o A027267     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A027267     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A027267 def A027267(n): return sum(T(n,k)*T(n,2*n-k) for k in (0..2*n))
%o A027267 [A027267(n) for n in (0..40)] # _G. C. Greubel_, Apr 12 2022
%Y A027267 Cf. A026536.
%K A027267 nonn
%O A027267 0,2
%A A027267 _Clark Kimberling_
%E A027267 More terms from _Sean A. Irvine_, Oct 26 2019