A026762 a(n) = T(2n-1,n-1), T given by A026758. Also T(2n+1,n+1), T given by A026747.

1, 4, 16, 66, 279, 1201, 5242, 23133, 103015, 462269, 2088146, 9487405, 43328580, 198798447, 915950385, 4236322720, 19661850045, 91549502656, 427539667095, 2002120576312, 9399659155395, 44234927105888, 208631813215116

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026747, A026758, A026759, A026760, A026761, 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-1,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[2n-1, 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-1, n-1) for n in (1..30)] # G. C. Greubel, Oct 31 2019