A027220 a(n) = Sum_{k=0..n} (k+1) * A026736(n,n-k).

1, 3, 8, 20, 52, 121, 301, 675, 1628, 3570, 8426, 18202, 42288, 90374, 207464, 439800, 1000194, 2106961, 4755715, 9967599, 22359788, 46670273, 104154703, 216643945, 481381746, 998346275, 2210037191, 4571884119, 10088030640

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026736.

Programs

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1,k-1] + T[n-2,k-1] + T[n-1,k], T[n-1,k-1] + T[n-1,k]]]; Table[Sum[(k+1)*T[n,n-k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Jul 19 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
[sum((k+1)*T(n,n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jul 19 2019