A026962 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.

1, 6, 24, 108, 406, 1572, 5961, 22788, 87209, 335010, 1290376, 4983162, 19286891, 74797176, 290586771, 1130716508, 4406049037, 17191077082, 67152699384, 262594530318, 1027851765350, 4026831276662, 15788979175102, 61954847930374, 243278117470476, 955907159445522

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

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

Cf. A026633, A026634, A026635, A026636, A026961, A026963, 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 *)
A262962[n_]:=Sum[T[n,k]*T[n,k+1], {k,0,n-1}];
Table[A262962[n], {n,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 A262962(n): return sum( T(n,k)*T(n,k+1) for k in range(n))
[A262962(n) for n in range(1,41)] # G. C. Greubel, Jun 23 2024

Extensions

More terms from Sean A. Irvine, Oct 20 2019