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A026559
a(n) = T(2*n, n-1), where T is given by A026552.
18
1, 3, 12, 45, 180, 721, 2940, 12069, 49935, 207691, 867900, 3640429, 15319395, 64643580, 273431408, 1158988141, 4921651521, 20934115963, 89173404140, 380355072153, 1624282578215, 6943928981859, 29715239620368, 127276313406125, 545605497876400, 2340694589348376, 10048952593607088, 43170264470594302
OFFSET
1,2
LINKS
FORMULA
a(n) = A026552(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)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n, n-1]];
Table[a[n], {n, 40}] (* G. C. Greubel, Dec 17 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026552
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+2)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-2)
[T(2*n, n-1) for n in (1..40)] # G. C. Greubel, Dec 17 2021
KEYWORD
nonn
EXTENSIONS
Terms a(20) onward added by G. C. Greubel, Dec 17 2021
STATUS
approved