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

1, 4, 17, 74, 327, 1461, 6584, 29879, 136391, 625731, 2883357, 13338421, 61920497, 288368511, 1346873365, 6307694990, 29613690966, 139352892908, 657163401162, 3105304341356, 14701236957028, 69722518168060, 331220099616432

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026752, A026753, A026754, A026755, A026756, A026757.

Programs

Maple

A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/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(A026747(2*n-1,n-1), n=1..30); # G. C. Greubel, Oct 29 2019

Mathematica

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 *)

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/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 29 2019