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a(n) = T(2n,n-1), T given by A026747.
11

%I #11 Oct 29 2019 21:09:42

%S 1,6,30,143,671,3132,14601,68101,318035,1487661,6971222,32727472,

%T 153926409,725264305,3423262180,16185240446,76648901377,363557014067,

%U 1726994886004,8215502584008,39135887682617,186676023857041,891557875400175

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

%H G. C. Greubel, <a href="/A026749/b026749.txt">Table of n, a(n) for n = 1..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,n-1), n=1..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, n-1], {n,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, n-1) for n in (1..30)] # _G. C. Greubel_, Oct 29 2019

%Y Cf. A026747, A026748, A026750, A026751, A026752, A026753, A026754, A026755, A026756, A026757.

%K nonn

%O 1,2

%A _Clark Kimberling_