A027074 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027052.

1, 1, 4, 22, 93, 389, 1570, 6144, 23629, 89551, 335430, 1244762, 4583293, 16765087, 60980096, 220724896, 795540601, 2856541663, 10222762962, 36475315442, 129796579409, 460757642587, 1632012075912, 5768986242408

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Programs

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif k=0 or k=2 or k=2*n then 1
    elif k=1 then 0
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq( add(T(n,k)*T(n,2*n-k), k=0..n-1), n=1..30); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n,k]*T[n,2*n-k], {k,0,n-1}], {n, 30}] (* G. C. Greubel, Nov 06 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2 or k==2*n): return 1
    elif (k==1): return 0
    else: return sum(T(n-1, k-j) for j in (1..3))
[sum(T(n,k)*T(n,2*n-k) for k in (0..n-1)) for n in (1..30)] # G. C. Greubel, Nov 06 2019