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!)
 A014062 a(n) = binomial(n^2, n). 39
 1, 1, 6, 84, 1820, 53130, 1947792, 85900584, 4426165368, 260887834350, 17310309456440, 1276749965026536, 103619293824707388, 9176358300744339432, 880530516383349192480, 91005567811177478095440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Roberts states that Gupta and Khare show that a(n) > A002110(n) for 2 < n < 1794 and that a(n) < A002110(n) for n >= 1794, where A002110(n) is the product of the first n primes. - T. D. Noe, Oct 03 2007 This sequence describes the number of ways to arrange n objects in an n X n array (for example, stars in a flag's field pattern). - Tom Young (mcgreg265(AT)msn.com), Jun 17 2010 It appears that a(n) == n (mod n^3) only if n is 1, an odd prime, the square of an odd prime, or the cube of an odd prime. - Gary Detlefs, Aug 06 2013; corrected by Michel Marcus, May 29 2015 REFERENCES H. Gupta and S. P. Khare, On C(k^2,k) and the product of the first k primes, Publ. Fac. Electrotechn. Belgrade, Ser. Math. Phys. 25-29 (1977) 577-598. J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 265. LINKS T. D. Noe, Table of n, a(n) for n=0..100 H. Alzer, J. Sandor, On a binomial coefficient and a product of prime numbers, Appl. An. Disc. Math. 5 (2011) 87-92. H. J. Brothers, Pascal's Prism: Supplementary Material. FORMULA a(n) ~ 1/sqrt(2*Pi) * (e*n)^(n - 1/2). - Charles R Greathouse IV, Jul 07 2007 a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n^2 - n, k). - Paul D. Hanna, Nov 18 2015 a(n) = (n+1)*A177234(n). - R. J. Mathar, Jan 25 2019 MATHEMATICA Table[Binomial[n^2, n], {n, 0, 22}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011 *) PROG (PARI) {a(n) = sum(k=0, n, binomial(n, k)*binomial(n^2-n, k))} for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Nov 18 2015 CROSSREFS Cf. A295773. Sequence in context: A277304 A128575 A322518 * A147626 A123312 A010794 Adjacent sequences: A014059 A014060 A014061 * A014063 A014064 A014065 KEYWORD nonn AUTHOR 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 7 13:02 EST 2022. Contains 358656 sequences. (Running on oeis4.)