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A260816 a(n) = floor(log(Catalan(n)). 1
0, 0, 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 64, 65, 66, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Largest integer m such that e^m < C(n), the n-th Catalan number, where e = exp(1) is the Euler number.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

FORMULA

a(n) = floor(log(C(n)).

For n >= 1,  a(n) is either floor(2*log(2)*n - (3/2)*log(n)) or floor(2*log(2)*n - (3/2)*log(n)) - 1. - Robert Israel, Aug 19 2015

EXAMPLE

a(5) = 3 because e^3 < C(3) = 42 < e^4.

MAPLE

seq(floor(log(binomial(2*n, n)/(n+1))), n=0 .. 100); # Robert Israel, Aug 19 2015

MATHEMATICA

f[n_] := Floor@ Log@ CatalanNumber@ n; Array[f, 70, 0] (* Robert G. Wilson v, Aug 18 2015 *)

PROG

(PARI) a(n)=floor(log(binomial(2*n, n)/(n+1)))

\\ Use realprecision > number of digits of C(max n)

(MAGMA) [Floor(Log(Binomial(2*n, n)/(n+1))): n in [0.. 65]]; // Vincenzo Librandi, Aug 20 2015

CROSSREFS

Cf. A000108, A001113.

Sequence in context: A039160 A175439 A048264 * A285598 A275804 A141825

Adjacent sequences:  A260813 A260814 A260815 * A260817 A260818 A260819

KEYWORD

nonn,less

AUTHOR

Stanislav Sykora, Jul 31 2015

STATUS

approved

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Last modified August 22 12:56 EDT 2017. Contains 290948 sequences.