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A026591
a(n) = T(2*n, n-1), where T is given by A026584.
17
1, 2, 9, 38, 140, 701, 2534, 13294, 48369, 258430, 947694, 5114572, 18872399, 102539204, 380143356, 2075658454, 7723000261, 42330184638, 157951859953, 868376395790, 3247811317907, 17899895038348, 67075896452000, 370442993383238, 1390392820937920, 7692166179956366, 28910883325637649, 160184255555687056
OFFSET
1,2
LINKS
FORMULA
a(n) = A026584(2*n, n-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]= Block[{$RecursionLimit= Infinity}, T[2*n, n-1]];
Table[a[n], {n, 1, 40}] (* G. C. Greubel, Dec 13 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)
[T(2*n, n-1) for n in (1..40)] # G. C. Greubel, Dec 13 2021
KEYWORD
nonn
EXTENSIONS
Terms a(19) onward from G. C. Greubel, Dec 13 2021
STATUS
approved