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 A268041 Table array: T(n,m) is the number of non-crossings matchings of curves embedded within an annulus with n exterior endpoints and m interior endpoints. 1
 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 4, 2, 3, 2, 3, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 10, 5, 7, 3, 7, 3, 7, 5, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 14, 17, 8, 14, 8, 14, 8, 17, 14, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 42, 48, 24, 38, 20, 34, 20, 38, 24, 48, 42, 80 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Table of n, a(n) for n=0..90. Paul Drube and Puttipong Pongtanapaisan, Annular Non-Crossing Matchings, Journal of Integer Sequences, Vol. 19 (2016), #16.2.4. 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))); a(n, m) = {if ((n+m) % 2, return (0)); if (n

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Last modified December 9 23:06 EST 2023. Contains 367696 sequences. (Running on oeis4.)