

A220314


binomial(2n,n)  (2n)^pi(n), where pi(n) is the number of primes <= n.


2



1, 2, 16, 6, 748, 804, 34984, 52666, 56356, 24756, 4448200, 5258468, 298515176, 441773704, 573882480, 472661434, 50189743924, 69289028796, 4312446874696, 6415753471180, 9144394121976, 11944124661496, 913956731941456, 1320357856911588
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(n) is strictly positive for all n >= 202. In fact, Erdos and EcklundEggleton proved more generally that binomial(k,n) > k^pi(n) if n >= 202 and k >= 2n. This theorem implies Sylvester's theorem. For the latter and references, see A213253.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..500


FORMULA

a(n) = A000984(n)  (2n)^A000720(n).


EXAMPLE

a(2) = binomial(4,2)  4^pi(2) = 6  4 = 2.


MATHEMATICA

Table[Binomial[2n, n]  (2n)^PrimePi[n], {n, 32}]


CROSSREFS

Cf. A000720, A000984, A213253.
Sequence in context: A336833 A211367 A351585 * A302206 A110008 A296728
Adjacent sequences: A220311 A220312 A220313 * A220315 A220316 A220317


KEYWORD

sign


AUTHOR

Jonathan Sondow, Dec 10 2012


STATUS

approved



