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A026763 a(n) = T(2n-1,n-2), T given by A026758.

%I A026763 #8 Nov 01 2019 03:53:38
%S A026763 1,7,38,190,918,4365,20594,96804,454362,2132121,10010203,47042042,
%T A026763 221337726,1042837195,4920447410,23250646651,110029743083,
%U A026763 521462857972,2474929099976,11762845907633,55982738983975,266789302547057
%N A026763 a(n) = T(2n-1,n-2), T given by A026758.
%H A026763 G. C. Greubel, <a href="/A026763/b026763.txt">Table of n, a(n) for n = 2..500</a>
%p A026763 T:= proc(n,k) option remember;
%p A026763    if n<0 then 0;
%p A026763    elif k=0 or k = n then 1;
%p A026763    elif type(n,'odd') and k <= (n-1)/2 then
%p A026763         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026763    else
%p A026763        procname(n-1,k-1)+procname(n-1,k) ;
%p A026763    end if ;
%p A026763 end proc;
%p A026763 seq(T(2*n-1,n-2), n=2..30); # _G. C. Greubel_, Oct 31 2019
%t A026763 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && k<=(n - 1)/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 31 2019 *)
%o A026763 (Sage)
%o A026763 @CachedFunction
%o A026763 def T(n, k):
%o A026763     if (n<0): return 0
%o A026763     elif (k==0 or k==n): return 1
%o A026763     elif (mod(n,2)==1 and k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026763     else: return T(n-1,k-1) + T(n-1,k)
%o A026763 [T(2*n-1, n-2) for n in (2..30)] # _G. C. Greubel_, Oct 31 2019
%Y A026763 Cf. A026758, A026759, A026760, A026761, A026762, A026764, A026765, A026766, A026767, A026768.
%K A026763 nonn
%O A026763 2,2
%A A026763 _Clark Kimberling_