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A189942
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Table, read by rows, of the number of quivers of type Ã_(n-1) according to the parameter k (n >= 2, 1 <= k <= [n/2]).
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0
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1, 2, 5, 4, 14, 12, 42, 36, 22, 132, 108, 100, 429, 349, 315, 172, 1430, 1144, 1028, 980, 4862, 3868, 3432, 3240, 1651, 16796, 13260, 11700, 10920, 10584, 58786, 46210, 40520, 37556, 36036, 18028, 208012, 162792, 142120, 130900, 124740, 121968
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OFFSET
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2,2
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COMMENTS
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Table 1, p. 15 of Bastian.
There is a bijection with dissections of an annulus [Hermund André Torkildsen]. - N. J. A. Sloane, Jan 31 2013
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REFERENCES
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Francois Bergeron, Gilbert Labelle and Pierre Leroux, Combinatorial species and tree-like structures, Encyclopedia of Mathematics and its Applications, vol. 67, Cambridge University Press, Cambridge, 1998, Translated from the 1994 French original by Margaret Readdy, With a foreword by Gian-Carlo Rota.
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LINKS
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EXAMPLE
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The table begins
===================================
n | r=1 | r=2 | r=3 | r=4 | r=5 |
===================================
n=2 1
n=3 2
n=4 5 4
n=5 14 12
n=6 42 36 22
n=7 132 108 100
n=8 429 349 315 172
n=9 1430 1144 1028 980
n=10 4862 3868 3432 3240 1651
===================================
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MATHEMATICA
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a[r_, r_] := 1/2 (Binomial[2 r, r]/2 + Sum[EulerPhi[k]/(4 r) Binomial[2 r/k, r/k]^2, {k, Divisors@r}]);
a[r_, s_] := 1/2 Sum[EulerPhi[k]/(r + s) Binomial[2 r/k, r/k] Binomial[2 s/k, s/k], {k, Intersection[Divisors@r, Divisors@s]}];
Table[a[r, n - r], {n, 2, 10}, {r, n/2}] // TableForm
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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