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A026751 a(n) = T(2n-1,n-1), T given by A026747.

%I A026751 #9 Oct 29 2019 21:11:09
%S A026751 1,4,17,74,327,1461,6584,29879,136391,625731,2883357,13338421,
%T A026751 61920497,288368511,1346873365,6307694990,29613690966,139352892908,
%U A026751 657163401162,3105304341356,14701236957028,69722518168060,331220099616432
%N A026751 a(n) = T(2n-1,n-1), T given by A026747.
%H A026751 G. C. Greubel, <a href="/A026751/b026751.txt">Table of n, a(n) for n = 1..500</a>
%p A026751 A026747 := proc(n,k) option remember;
%p A026751    if k=0 or k = n then 1;
%p A026751    elif type(n,'even') and k <= n/2 then
%p A026751         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026751    else
%p A026751        procname(n-1,k-1)+procname(n-1,k) ;
%p A026751    end if ;
%p A026751 end proc:
%p A026751 seq(A026747(2*n-1,n-1), n=1..30); # _G. C. Greubel_, Oct 29 2019
%t A026751 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-1], {n,30}] (* _G. C. Greubel_, Oct 29 2019 *)
%o A026751 (Sage)
%o A026751 @CachedFunction
%o A026751 def T(n, k):
%o A026751     if (k==0 or k==n): return 1
%o A026751     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 A026751     else: return T(n-1,k-1) + T(n-1,k)
%o A026751 [T(2*n-1, n-1) for n in (1..30)] # _G. C. Greubel_, Oct 29 2019
%Y A026751 Cf. A026747, A026748, A026749, A026750, A026752, A026753, A026754, A026755, A026756, A026757.
%K A026751 nonn
%O A026751 1,2
%A A026751 _Clark Kimberling_