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A026772 a(n) = T(2n, n-2), T given by A026769.

%I A026772 #7 Nov 01 2019 22:22:48
%S A026772 1,10,71,444,2616,14938,83821,465654,2572166,14164320,77886902,
%T A026772 428113940,2353823912,12950837432,71326701751,393289209772,
%U A026772 2171308560036,12003376308370,66445540183348,368304502202306,2044177115127750
%N A026772 a(n) = T(2n, n-2), T given by A026769.
%H A026772 G. C. Greubel, <a href="/A026772/b026772.txt">Table of n, a(n) for n = 2..500</a>
%p A026772 T:= proc(n,k) option remember;
%p A026772    if n<0 then 0;
%p A026772    elif k=0 or k=n then 1;
%p A026772    elif n=2 and k=1 then 2;
%p A026772    elif k <= (n-1)/2 then
%p A026772         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026772    else
%p A026772        procname(n-1,k-1)+procname(n-1,k) ;
%p A026772    end if ;
%p A026772 end proc;
%p A026772 seq(T(2*n, n-2), n=2..30); # _G. C. Greubel_, Nov 01 2019
%t A026772 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[k<=(n-1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]]; Table[T[2*n, n-2], {n,2,30}] (* _G. C. Greubel_, Nov 01 2019 *)
%o A026772 (Sage)
%o A026772 @CachedFunction
%o A026772 def T(n, k):
%o A026772     if (k==0 or k==n): return 1
%o A026772     elif (n==2 and k==1): return 2
%o A026772     elif (k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026772     else: return T(n-1,k-1) + T(n-1,k)
%o A026772 [T(2*n, n-2) for n in (2..30)] # _G. C. Greubel_, Nov 01 2019
%Y A026772 Cf. A026769, A026770, A026771, A026773, A026774, A026775, A026776, A026777, A026778, A026779.
%K A026772 nonn
%O A026772 2,2
%A A026772 _Clark Kimberling_