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A027262 a(n) = self-convolution of row n of array T given by A026519.

%I A027262 #13 Dec 22 2021 07:03:56
%S A027262 1,3,8,58,196,1608,5774,48924,180772,1553940,5837908,50618184,
%T A027262 192239854,1676640462,6416509142,56201554888,216309089956,
%U A027262 1900789437276,7347943049432,64734185205960,251119894730596,2216888144737508,8624336421678788,76265067399850848,297394187356638766
%N A027262 a(n) = self-convolution of row n of array T given by A026519.
%H A027262 G. C. Greubel, <a href="/A027262/b027262.txt">Table of n, a(n) for n = 0..1000</a>
%F A027262 a(n) = Sum_{k=0..2*n} A026519(n, k)*A026519(n, 2*n-k).
%t A027262 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/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 = A026519 *)
%t A027262 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n,k]*T[n,2*n-k], {k,0,2*n}] ];
%t A027262 Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Dec 21 2021 *)
%o A027262 (Sage)
%o A027262 @CachedFunction
%o A027262 def T(n,k): # T = A026519
%o A027262     if (k<0 or k>2*n): return 0
%o A027262     elif (k==0 or k==2*n): return 1
%o A027262     elif (k==1 or k==2*n-1): return (n+1)//2
%o A027262     elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o A027262     else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A027262 @CachedFunction
%o A027262 def a(n): return sum( T(n,k)*T(n,2*n-k) for k in (0..2*n) )
%o A027262 [a(n) for n in (0..40)] # _G. C. Greubel_, Dec 22 2021
%Y A027262 Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026532, A026533, A026534, A027263, A027264, A027265, A027266.
%K A027262 nonn
%O A027262 0,2
%A A027262 _Clark Kimberling_
%E A027262 More terms from _Sean A. Irvine_, Oct 26 2019