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A027283
a(n) = Sum_{k=0..2*n-1} T(n,k) * T(n,k+1), with T given by A026584.
16
0, 6, 26, 206, 1100, 7314, 42920, 274010, 1677332, 10616070, 66290046, 419754586, 2648500908, 16818685050, 106781976774, 680250643910, 4337083126232, 27709045093274, 177213890858938, 1135003956744310, 7276652578220372, 46702733068082702, 300013046145979184
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=0..2*n-1} A026584(n,k) * A026584(n,k+1).
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Sum[T[n, k]*T[n, k+1], {k, 0, 2*n-1}];
Table[a[n], {n, 1, 40}] (* G. C. Greubel, Dec 15 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026584
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
@CachedFunction
def A027283(n): return sum(T(n, j)*T(n, j+1) for j in (0..2*n-1))
[A027283(n) for n in (1..40)] # G. C. Greubel, Dec 15 2021
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 26 2019
STATUS
approved