A027044 a(n) = Sum_{k=0..2n} (k+1) * A027023(n,2n-k).

1, 6, 19, 56, 165, 486, 1435, 4248, 12601, 37438, 111367, 331608, 988181, 2946662, 8791447, 26241632, 78359825, 234069830, 699404127, 2090385216, 6249236653, 18686125070, 55884824535, 167164064984, 500102988889

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