A026785 a(n) = T(2n-1, n-2), T given by A026780.

1, 9, 60, 361, 2076, 11672, 64842, 357897, 1968788, 10813804, 59372770, 326086492, 1792293014, 9861375614, 54324086446, 299651439321, 1655124211372, 9154654655044, 50704627346170, 281214708137032, 1561706813618886

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..500

Crossrefs

Cf. A026780, A026781, A026782, A026783, A026784, A026786, A026787, A026788, A026789, A026790.

Programs

Maple

T:= proc(n,k) option remember;
    if n<0 then 0;
    elif k=0 or k =n then 1;
    elif 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) ;
    fi ;
end proc:
seq(T(2*n-1,n-2), n=2..30); # G. C. Greubel, Nov 02 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[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[2*n-1, n-2], {n,2,30}] (* G. C. Greubel, Nov 02 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (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-2) for n in (2..30)] # G. C. Greubel, Nov 02 2019