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A026546 a(n) = T(2n-1,n-2), T given by A026536.

%I A026546 #8 Apr 12 2022 01:35:31
%S A026546 1,2,10,36,150,602,2485,10256,42687,178300,747912,3146936,13278707,
%T A026546 56163758,238052050,1010857520,4299545769,18314436414,78115839734,
%U A026546 333583225740,1426072211137,6102528959956,26138050436822,112046904456640,480686415837200,2063641522153406,8865329237958042,38108667849379540
%N A026546 a(n) = T(2n-1,n-2), T given by A026536.
%H A026546 G. C. Greubel, <a href="/A026546/b026546.txt">Table of n, a(n) for n = 2..300</a>
%F A026546 a(n) = A026536(2*n-1, n-2).
%t A026546 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 A026546 Table[T[2n-1, n-2], {n,2,40}] (* _G. C. Greubel_, Apr 11 2022 *)
%o A026546 (SageMath)
%o A026546 @CachedFunction
%o A026546 def T(n, k): # A026536
%o A026546     if k < 0 or n < 0: return 0
%o A026546     elif k == 0 or k == 2*n: return 1
%o A026546     elif k == 1 or k == 2*n-1: return n//2
%o A026546     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026546     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026546 def A026546(n): return T(2*n-1, n-2)
%o A026546 [A026546(n) for n in (2..40)] # _G. C. Greubel_, Apr 11 2022
%Y A026546 Cf. A026536.
%K A026546 nonn
%O A026546 2,2
%A A026546 _Clark Kimberling_
%E A026546 Terms a(20) onward added by _G. C. Greubel_, Apr 11 2022