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A026545 a(n) = T(2n-1, n-1), T given by A026536.

%I A026545 #8 Apr 12 2022 01:35:36
%S A026545 1,1,6,19,79,306,1247,5069,20889,86479,360205,1506462,6324176,
%T A026545 26630423,112439094,475838291,2017827545,8572102713,36474080228,
%U A026545 155418445421,663102388605,2832471934357,12111891668431,51841780973922,222092855692496,952237575555176,4085873505697131,17544024146446621
%N A026545 a(n) = T(2n-1, n-1), T given by A026536.
%H A026545 G. C. Greubel, <a href="/A026545/b026545.txt">Table of n, a(n) for n = 1..300</a>
%F A026545 a(n) = A026536(2*n-1, n-1).
%t A026545 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 A026545 Table[T[2*n-1, n-1], {n,40}] (* _G. C. Greubel_, Apr 11 2022 *)
%o A026545 (SageMath)
%o A026545 @CachedFunction
%o A026545 def T(n, k): # A026536
%o A026545     if k < 0 or n < 0: return 0
%o A026545     elif k == 0 or k == 2*n: return 1
%o A026545     elif k == 1 or k == 2*n-1: return n//2
%o A026545     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026545     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026545 def A026545(n): return T(2*n-1, n-1)
%o A026545 [A026545(n) for n in (1..40)] # _G. C. Greubel_, Apr 11 2022
%Y A026545 Cf. A026536.
%K A026545 nonn
%O A026545 1,3
%A A026545 _Clark Kimberling_
%E A026545 Terms a(20) onward added by _G. C. Greubel_, Apr 11 2022