A026621 a(n) = A026615(n, floor(n/2)).

1, 1, 3, 5, 10, 17, 34, 60, 120, 217, 434, 798, 1596, 2970, 5940, 11154, 22308, 42185, 84370, 160446, 320892, 613054, 1226108, 2351440, 4702880, 9048522, 18097044, 34916300, 69832600, 135059220, 270118440, 523521630, 1047043260, 2033066025, 4066132050, 7908332190

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026622.

Cf. A026623, A026624, A026625, A026956, A026957, A026958, A026959.

Cf. A026960.

Programs

Magma

I:=[1,3]; [1] cat [n le 2 select I[n] else 2*((49*n^2-287*n+360 )*Self(n-1) + 2*(n-3)*(7*n-8)*(7*n-17)*Self(n-2) )/((n+1)*(7*n-24)*(7*n-15)) : n in [1..40]]; // G. C. Greubel, Jun 13 2024

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, 2*n-1, T[n -1,k-1] +T[n-1,k]]]; (* T = A026615 *)
Table[T[n, Floor[n/2]], {n,0,40}] (* G. C. Greubel, Jun 13 2024 *)

SageMath

@CachedFunction
def T(n, k): # T = A026615
    if k==0 or k==n: return 1
    elif k==1 or k==n-1: return 2*n-1
    else: return T(n-1, k-1) + T(n-1, k)
def A026621(n): return T(n, int(n//2))
[A026621(n) for n in range(41)] # G. C. Greubel, Jun 13 2024

Formula

a(n) = 2*( (49*n^2 - 287*n + 360)*a(n-1) + 2*(n-3)*(7*n-8)*(7*n-17)*a(n-2) )/((n+1)*(7*n-24)*(7*n-15)) for n > 2. - G. C. Greubel, Jun 13 2024