A026782 a(n) = T(2n,n-1), T given by A026780.

1, 7, 40, 217, 1158, 6150, 32656, 173719, 926664, 4958556, 26619438, 143365880, 774562478, 4197344582, 22810572062, 124300860689, 679081142350, 3718894341450, 20412141531664, 112276061739814, 618806031336236, 3416954495002676

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026780, A026781, A026783, A026784, A026785, 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,n-1), n=1..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, n-1], {n, 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, n-1) for n in (1..30)] # G. C. Greubel, Nov 02 2019