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A027265 a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A026519.

%I A027265 #17 Dec 22 2021 07:46:16
%S A027265 24,104,954,3786,33648,131264,1159844,4508580,39809076,154773696,
%T A027265 1367463642,5323519838,47082494816,183586707648,1625447736120,
%U A027265 6348284151024,56265306436584,220081449149440,1952476424575980,7647723960962932,67907006619888744,266322435212031984
%N A027265 a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A026519.
%H A027265 G. C. Greubel, <a href="/A027265/b027265.txt">Table of n, a(n) for n = 3..1000</a>
%F A027265 a(n) = Sum_{k=0..2n-3} A026519(n,k) * A026519(n,k+3).
%t A027265 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 A027265 a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}] ];
%t A027265 Table[a[n], {n, 3, 40}] (* _G. C. Greubel_, Dec 21 2021 *)
%o A027265 (Sage)
%o A027265 @CachedFunction
%o A027265 def T(n,k): # T = A026519
%o A027265     if (k<0 or k>2*n): return 0
%o A027265     elif (k==0 or k==2*n): return 1
%o A027265     elif (k==1 or k==2*n-1): return (n+1)//2
%o A027265     elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o A027265     else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A027265 @CachedFunction
%o A027265 def a(n): return sum( T(n,k)*T(n,k+3) for k in (0..2*n-3) )
%o A027265 [a(n) for n in (3..40)] # _G. C. Greubel_, Dec 21 2021
%Y A027265 Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026532, A026533, A026534, A027262, A027263, A027264, A027266.
%K A027265 nonn
%O A027265 3,1
%A A027265 _Clark Kimberling_
%E A027265 More terms from _Sean A. Irvine_, Oct 26 2019