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%I #7 Nov 02 2019 20:00:13
%S 1,5,24,117,580,2916,14834,76221,395048,2063104,10847078,57373672,
%T 305110106,1630489090,8751851866,47166202181,255128842340,
%U 1384688987728,7538592535170,41159292861980,225315261459390,1236441650047554
%N a(n) = T(2n-1, n-1), T given by A026780.
%H G. C. Greubel, <a href="/A026784/b026784.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-1,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-1, 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-1, n-1) for n in (1..30)] # _G. C. Greubel_, Nov 02 2019
%Y Cf. A026780, A026781, A026782, A026783, A026785, A026786, A026787, A026788, A026789, A026790.
%K nonn
%O 1,2
%A _Clark Kimberling_
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