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a(n) = T(2n,n), T given by A026747.
10

%I #11 Oct 30 2019 01:11:37

%S 1,3,11,44,184,790,3452,15278,68290,307696,1395696,6367199,29193025,

%T 134442102,621609060,2884432810,13428450520,62703991531,293606387095,

%U 1378309455352,6485734373020,30586630485443,144544075759391,684395988590939

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

%H G. C. Greubel, <a href="/A026748/b026748.txt">Table of n, a(n) for n = 0..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), n=0..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], {n,0,30}] (* _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) for n in (0..30)] # _G. C. Greubel_, Oct 29 2019

%Y Cf. A026747, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026756, A026757.

%K nonn

%O 0,2

%A _Clark Kimberling_