A026963 a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026626.

1, 8, 52, 224, 987, 3980, 16057, 63732, 252424, 996332, 3927977, 15471622, 60915547, 239794516, 943946193, 3716205884, 14632901696, 57631689776, 227042423404, 894698122022, 3526753844436, 13906101471344, 54848887043366, 216402159510134, 854053133294062, 3371593602442500

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.

Cf. A026633, A026634, A026635, A026636, A026961, A026962, A026964.

Cf. A026965.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[3*n/2], T[n-1,k-1] +T[n-1,k]]]; (* T = A026626 *)
A262963[n_]:= Sum[T[n,k]*T[n,k+2], {k,0,n-2}];
Table[A262963[n], {n,2,40}] (* G. C. Greubel, Jun 23 2024 *)

SageMath

@CachedFunction
def T(n, k): # T = A026626
    if (k==0 or k==n): return 1
    elif (k==1 or k==n-1): return int(3*n//2)
    else: return T(n-1, k-1) + T(n-1, k)
def A262963(n): return sum( T(n,k)*T(n,k+2) for k in range(n-1))
[A262963(n) for n in range(2,41)] # G. C. Greubel, Jun 23 2024

Extensions

More terms from Sean A. Irvine, Oct 20 2019