A081399 Bigomega of the n-th Catalan number: a(n) = A001222(A000108(n)).

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

M. F. Hasler, Table of n, a(n) for n = 0..3000.

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

Crossrefs

Cf. A001222, A000108, A022559, A023816, A048621, A081405, A120626, A137686-A137687.

Cf. A080405.

Sequence in context: A362024 A030583 A030563 * A221108 A205554 A373579

Adjacent sequences: A081396 A081397 A081398 * A081400 A081401 A081402

Keyword

nonn,easy

Author

Labos Elemer, Mar 28 2003

Extensions

Edited and extended by M. F. Hasler, Feb 06 2008

Status

approved