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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A268042 a(n) = Ann(2n) where Ann(n) is the number of annular non-crossing matchings with n total endpoints. 0
 1, 3, 8, 20, 57, 166, 538, 1762, 6045, 21040, 74628, 267598, 970134, 3544416, 13043650, 48283236, 179665425, 671564330, 2520312810, 9492124534, 35863942748, 135893383596, 516258841134, 1965906973886, 7502329984510, 28687263026656, 109893836400756, 421684916479018 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..27. Paul Drube and Puttipong Pongtanapaisan, Annular Non-Crossing Matchings, Journal of Integer Sequences, Vol. 19 (2016), #16.2.4. FORMULA a(n) = Sum_{i+j=n} A268041(i, j). PROG (PARI) tnnk(n, k) = if (!n && !k, 1, sumdiv(gcd(n, k), d, eulerphi(d)*binomial((2*n+k)/d, n/d))/(2*n+k)); tnmk(n, m, k) = if (k==0, tnnk(n, 0)*tnnk(m, 0), k*sumdiv(gcd(k, gcd(n, m)), d, eulerphi(d)*binomial((2*n+k)/d, n/d)*binomial((2*m+k)/d, m/d))/((2*n+k)*(2*m+k))); ann(n, m) = {if ((n+m) % 2, return (0)); if (n

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 March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)