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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
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<m, return (ann(m, n))); sum(k=0, m, if (!((n-k)%2) && !((m-k)%2), tnmk((n-k)/2, (m-k)/2, k), 0)); }
a(n) = sum(k=0, n, ann(n-k, k));
CROSSREFS
Sequence in context: A271843 A122228 A018790 * A009436 A354519 A302674
KEYWORD
nonn
AUTHOR
Michel Marcus, Jan 25 2016
STATUS
approved

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