A026760 a(n) = T(2n, n-1), T given by A026758.

1, 5, 23, 104, 469, 2119, 9607, 43727, 199819, 916631, 4220267, 19497608, 90370622, 420136173, 1958787580, 9156770130, 42912496696, 201579245739, 949002525067, 4477049676288, 21162505063028, 100217666089863, 475421115762173

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A026758, A026759, A026761, A026762, A026763, A026764, A026765, A026766, A026767, A026768.

Programs

Maple

T:= proc(n,k) option remember;
   if n<0 then 0;
   elif k=0 or k = n then 1;
   elif type(n,'odd') and k <= (n-1)/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc;
seq(T(2*n,n-1), n=1..30); # G. C. Greubel, Oct 31 2019

Mathematica

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[2 n, n-1], {n, 0, 30}] (* G. C. Greubel, Oct 31 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    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)
    else: return T(n-1,k-1) + T(n-1,k)
[T(2*n, n-1) for n in (1..30)] # G. C. Greubel, Oct 31 2019