A027041 a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027023.

1, 2, 5, 20, 77, 306, 1209, 4656, 17713, 66618, 248025, 916020, 3359789, 12250026, 44435997, 160466304, 577185745, 2068826290, 7392167585, 26338879556, 93609302941, 331924381218, 1174482354493, 4147807582672, 14622567051025, 51466158436298, 180869949252245, 634753692067716

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Maple

T:= proc(n, k) option remember;
      if k<3 or k=2*n then 1
    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), n=0..30); # G. C. Greubel, Nov 04 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[T[n,k]*T[n,2*n-k], {k,0,n}], {n,0,30}] (* G. C. Greubel, Nov 04 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k<3 or k==2*n): return 1
    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)) for n in (0..30)] # G. C. Greubel, Nov 04 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019