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%I #8 Nov 01 2019 03:53:38
%S 1,7,38,190,918,4365,20594,96804,454362,2132121,10010203,47042042,
%T 221337726,1042837195,4920447410,23250646651,110029743083,
%U 521462857972,2474929099976,11762845907633,55982738983975,266789302547057
%N a(n) = T(2n-1,n-2), T given by A026758.
%H G. C. Greubel, <a href="/A026763/b026763.txt">Table of n, a(n) for n = 2..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 type(n,'odd') and k <= (n-1)/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 end if ;
%p end proc;
%p seq(T(2*n-1,n-2), n=2..30); # _G. C. Greubel_, Oct 31 2019
%t T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && 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[2n-1, n-2], {n, 2, 30}] (* _G. C. Greubel_, Oct 31 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 (mod(n,2)==1 and k<=(n-1)/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-2) for n in (2..30)] # _G. C. Greubel_, Oct 31 2019
%Y Cf. A026758, A026759, A026760, A026761, A026762, A026764, A026765, A026766, A026767, A026768.
%K nonn
%O 2,2
%A _Clark Kimberling_
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