A026771 a(n) = T(2n,n-1), T given by A026769.

1, 6, 31, 156, 784, 3962, 20173, 103522, 535294, 2787700, 14613710, 77072816, 408737760, 2178631156, 11666175215, 62734622764, 338660977020, 1834690352066, 9971834477972, 54361287536706, 297170702049966, 1628670524735842

Offset

1,2

Links

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

Maple

T:= proc(n, k) option remember;
   if n<0 then 0;
   elif k=0 or k=n then 1;
   elif n=2 and k=1 then 2;
   elif 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, Nov 01 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[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, 30}] (* G. C. Greubel, Nov 01 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (n==2 and k==1): return 2
    elif (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, Nov 01 2019

Crossrefs

Cf. A026769, A026770, A026772, A026773, A026774, A026775, A026776, A026777, A026778, A026779.

Sequence in context: A026705 A243874 A003463 * A289788 A065096 A077352

Adjacent sequences: A026768 A026769 A026770 * A026772 A026773 A026774

Keyword

nonn

Author

Clark Kimberling

Status

approved