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A026962
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.
16
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
1,2
LINKS
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 *)
PROG
(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
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 20 2019
STATUS
approved