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a(n) = T(2n,n-2), T given by A026747.
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%I #9 Oct 29 2019 21:11:03

%S 1,9,58,329,1753,9020,45442,225860,1112543,5446607,26550968,129042976,

%T 625860205,3031021096,14664729519,70906318405,342717456708,

%U 1656208470644,8003645557573,38681730323747,186985728069661,904119336235884

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

%H G. C. Greubel, <a href="/A026750/b026750.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,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, 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, n-2) for n in (2..30)] # _G. C. Greubel_, Oct 29 2019

%Y Cf. A026747, A026748, A026749, A026751, A026752, A026753, A026754, A026755, A026756, A026757.

%K nonn

%O 2,2

%A _Clark Kimberling_