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!)
 A014495 Central binomial coefficient - 1. 11
 0, 0, 1, 2, 5, 9, 19, 34, 69, 125, 251, 461, 923, 1715, 3431, 6434, 12869, 24309, 48619, 92377, 184755, 352715, 705431, 1352077, 2704155, 5200299, 10400599, 20058299, 40116599, 77558759, 155117519, 300540194, 601080389, 1166803109, 2333606219, 4537567649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For n > 0: sum of positive elements in row (n-1) of triangle A214292. - Reinhard Zumkeller, Jul 12 2012 Number of Young tableaux with n cells and 2 rows. Also number of self-inverse permutations in S_n with longest increasing subsequence of length 2. The a(4) = 5 permutations are 1432, 2143, 3214, 3412, 4231 and the a(5) = 9 permutations are 15432, 21543, 32154, 35142, 42513, 43215, 45312, 52431, 53241. - Alois P. Heinz, Oct 03 2012 Number of nonempty subsets of {1,2,...,n} that contain the same number of even and odd numbers. For example, a(5)=9 and the 9 subsets are {1,2}, {1,4}, {2,3}, {2,5}, {3,4}, {4,5}, {1,2,3,4}, {1,2,4,5}, {2,3,4,5}. - Enrique Navarrete, Feb 10 2018 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A001405(n)-1. a(n) = C(n-1,floor((n-1)/2))-1. - Alois P. Heinz, Oct 03 2012 n*a(n)-2*a(n-1)-4*(n-2)*a(n-2) = 3*n-6 with n>1, a(0)=a(1)=0. - Bruno Berselli, Oct 03 2012 D-finite with recurrence: -(n+1)*(n-2)*a(n) +(n^2+n-4)*a(n-1) +2*(n-1)*(2*n-5)*a(n-2) -4*(n-1)*(n-2)*a(n-3)=0. - Conjectured by R. J. Mathar, Jan 04 2017, confirmed by Robert Israel, Feb 11 2018 G.f.: (x+1)/(2*x*(x-1)) - sqrt(1-4*x^2)/(2*x*(2*x-1)). - Robert Israel, Feb 11 2018 MAPLE a:= n-> binomial(n, iquo(n, 2))-1: seq(a(n), n=0..40); # Alois P. Heinz, Oct 03 2012 MATHEMATICA Table[Binomial[n - 1, Floor[(n - 1)/2]] - 1, {n, 0, 50}] (* Bruno Berselli, Oct 03 2012 *) PROG (Maxima) A014495(n):=binomial(n-1, floor((n-1)/2))-1\$ makelist(A014495(n), n, 1, 30); /* Martin Ettl, Nov 01 2012 */ (Magma) [Binomial(n-1, Floor((n-1)/2))-1: n in [1..50]]; // Vincenzo Librandi, Feb 11 2018 CROSSREFS Cf. A001405, A037952 (first differences). a(n) = A094718(n, n) = A094718(n-1, n)+1. a(n) = A047884(n, 2) for n>=2. - Alois P. Heinz, Oct 03 2012 Cf. A214292. Sequence in context: A073118 A048082 A089089 * A056326 A280247 A261049 Adjacent sequences: A014492 A014493 A014494 * A014496 A014497 A014498 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Denis Pochuev (denis(AT)cdc.Informatik.TH-Darmstadt.de) 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 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)