A027042 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027023.

1, 4, 11, 52, 225, 920, 3695, 14464, 55593, 210776, 789995, 2933380, 10807625, 39556316, 143958335, 521340016, 1879901265, 6753038624, 24176722555, 86294777316, 307179518193, 1090771084252, 3864614381391, 13664531314176, 48225146757337, 169905685271956, 597661852713467

Offset

1,2

Links

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

Crossrefs

Sequence in context: A355337 A218957 A149317 * A051770 A262006 A209110

Adjacent sequences: A027039 A027040 A027041 * A027043 A027044 A027045

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved