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a(n) = T(2n-1,n-2), T given by A026747.
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%I #9 Oct 29 2019 21:10:16

%S 1,7,39,201,1000,4885,23621,113543,543895,2600204,12417829,59278440,

%T 282969385,1351124510,6454283276,30849969965,147555219782,

%U 706274470775,3383203356648,16219148141581,77817618006364,373661751926702

%N a(n) = T(2n-1,n-2), T given by A026747.

%H G. C. Greubel, <a href="/A026752/b026752.txt">Table of n, a(n) for n = 2..500</a>

%p A026747 := proc(n,k) option remember;

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

%p elif type(n,'even') and 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 end if ;

%p end proc:

%p seq(A026747(2*n-1,n-2), n=2..30); # _G. C. Greubel_, Oct 29 2019

%t T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && 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] ]]; Table[T[2n-1, n-2], {n,2,30}] (* _G. C. Greubel_, Oct 29 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

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

%o elif (mod(n,2)==0 and 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-2) for n in (2..30)] # _G. C. Greubel_, Oct 29 2019

%Y Cf. A026747, A026748, A026749, A026750, A026751, A026753, A026754, A026755, A026756, A026757.

%K nonn

%O 2,2

%A _Clark Kimberling_