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

0,2

Links

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A189734 A221678 A297350 * A355866 A186767 A009737

Adjacent sequences: A027038 A027039 A027040 * A027042 A027043 A027044

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved