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A081399
Bigomega of the n-th Catalan number: a(n) = A001222(A000108(n)).
5
0, 0, 1, 1, 2, 3, 4, 3, 4, 4, 5, 5, 6, 7, 9, 7, 8, 8, 10, 9, 10, 10, 11, 11, 11, 12, 12, 11, 13, 13, 14, 11, 13, 14, 14, 13, 14, 14, 16, 15, 16, 18, 19, 19, 19, 19, 21, 19, 20, 19, 21, 20, 21, 21, 21, 19, 20, 20, 22, 22, 24, 25, 25, 23, 23, 23, 24, 24, 27, 26, 27, 25, 27, 28, 29, 28
OFFSET
0,5
COMMENTS
It is easy to show that a(n) is between n/log(n) and 2n/log(n) (for n>n0), cf. [Campbell 1984]. The sequence A137687, roughly the middle of this interval, is a fair approximation for A081399. See A137686 for the (signed) difference of the two sequences.
LINKS
Douglas M. Campbell, The Computation of Catalan Numbers, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.
FORMULA
a(n)=A001222[A000108(n)]
MAPLE
with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(2*n, n)/(1+n)) fi end: seq(a(n), n=0..75); # Zerinvary Lajos, Apr 11 2008
MATHEMATICA
a[n_] := PrimeOmega[ CatalanNumber[n]]; Table[a[n], {n, 0, 75}] (* Jean-François Alcover, Jul 02 2013 *)
PROG
(PARI) A081399(n)=bigomega(prod(i=2, n, (n+i)/i)) \\ M. F. Hasler, Feb 06 2008
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Mar 28 2003
EXTENSIONS
Edited and extended by M. F. Hasler, Feb 06 2008
STATUS
approved