A027046 a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027023.

1, 2, 5, 16, 65, 286, 1305, 6232, 30377, 150178, 750937, 3785904, 19215865, 98086646, 503087741, 2591128000, 13394476993, 69466312210, 361315132065, 1884242109256, 9849626540337, 51599350440694, 270851460356973

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,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,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,n+k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 04 2019