A027047 a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027023.

2, 8, 50, 336, 2418, 18088, 138850, 1086016, 8617122, 69159896, 560290322, 4574820624, 37603654098, 310873702392, 2582964183874, 21556333188288, 180609299685954, 1518572497996568, 12808849866774002, 108351496132761104, 918964407713589618, 7812768025080427672

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<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,k+1), k=0..2*n-1), n=1..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,k+1], {k,0,2*n-1}], {n,1,30}] (* 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,k+1) for k in (0..2*n-1)) for n in (1..30)] # G. C. Greubel, Nov 04 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019