The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Ecklund-Eggleton 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 01:13 EST 2022. Contains 358453 sequences. (Running on oeis4.)