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
KEYWORD
nonn,less
AUTHOR
Stanislav Sykora, Jul 31 2015
STATUS
approved