%I #9 Nov 02 2019 19:59:54

%S 1,7,40,217,1158,6150,32656,173719,926664,4958556,26619438,143365880,

%T 774562478,4197344582,22810572062,124300860689,679081142350,

%U 3718894341450,20412141531664,112276061739814,618806031336236,3416954495002676

%N a(n) = T(2n,n-1), T given by A026780.

%H G. C. Greubel, <a href="/A026782/b026782.txt">Table of n, a(n) for n = 1..500</a>

%p T:= proc(n,k) option remember;

%p if n<0 then 0;

%p elif k=0 or k =n then 1;

%p elif k <= n/2 then

%p procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;

%p else

%p procname(n-1,k-1)+procname(n-1,k) ;

%p fi ;

%p end proc:

%p seq(T(2*n,n-1), n=1..30); # _G. C. Greubel_, Nov 02 2019

%t T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[k<=n/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]];

%t Table[T[2*n, n-1], {n, 30}] (* _G. C. Greubel_, Nov 02 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o if (n<0): return 0

%o elif (k==0 or k==n): return 1

%o elif (k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)

%o else: return T(n-1,k-1) + T(n-1,k)

%o [T(2*n, n-1) for n in (1..30)] # _G. C. Greubel_, Nov 02 2019

%Y Cf. A026780, A026781, A026783, A026784, A026785, A026786, A026787, A026788, A026789, A026790.

%K nonn

%O 1,2

%A _Clark Kimberling_