

A268041


Table array: T(n,m) is the number of noncrossings 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
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OFFSET

0,11


LINKS



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<m, return (a(m, n))); sum(k=0, m, if (!((nk)%2) && !((mk)%2), tnmk((nk)/2, (mk)/2, k), 0)); }


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



